Classification of RPS-like Games

An "RPS-like game" is a two-person zero-sum game which is symmetric and provides a single positive payoff for all non-equal outcomes. More clearly, an RPS-like game with N options is defined by an NxN payoff matrix P, where P(a,b) = -P(b,a) for all a,b; and all off-diagonal elements of the matrix are either -1 or +1. Calling the two players Alice and Bob, the symmetry tells us that Alice's and Bob's optimal mixed strategies will be identical and the expected value of the game is zero.

It is my intention in this note to list the possible structures of the simplest RPS-like games. Each structure will be defined by the list of probabilities for its optimal mixed strategy. A subscript on that probability denotes how many opponent moves the given move beats.

I provide a tarball of the source code I used to produce the results for N > 5.

General framework

The classic N=3 RPS game has three moves called 'Rock,' 'Paper,' Scissors,' but we will need names for seven different moves for N=7. Let's adopt the following general framework, based on Five Elements (F, I, T, E, W) and Two Agents (M, S) obeying these rules:

• a. Fire melts Iron and consumes Tree.
• b. Iron chops Tree and ploughs Earth.
• c. Tree eats Earth and drinks Water.
• d. Earth dilutes Water and Fire.
• e. Water quenches Fire and rusts Iron.
• f. Master governs Slave, but is old and succumbs to all the Elements except as specified.
• g. Slave is hardy and exploits all the Elements except as specified.

Classification of RPS-like Games, N=3

There are two cases when only three moves are available:

1. (1₂, 0₁, 0₀) ÷ 1   ::   one strategy dominates
2. (1₁, 1₁, 1₁) ÷ 3   ::   this is the classic rock-paper-scissors game. Instead of R-P-S, you can use (Fire, Water, Tree), or any of several other trios, to conform to our general framework.

Classification of RPS-like Games, N=4

There are no additional cases with a fourth option. One of the possible plays will always be dominated. This is the case for any even N as I show in a final section.

Classification of RPS-like Games, N=5

The N=3 cases are still possible; we need show only the additional cases where all five moves are selected with non-zero probability.

3. (1₂, 1₂, 1₂, 1₂, 1₂) ÷ 5   ::   This is Fire/Iron/Tree/Earth/Water in the general framework.
4. (3₃, 3₁, 1₂, 1₂, 1₂) ÷ 9   ::   this can be viewed as cascaded RPS, the five moves being (a) 'Rock', (b) 'Paper', (c) 'Scissors and if we tie, then R', (d) 'Scissors and if we tie, then P', (e) 'Scissors and if we tie, then S'. This can be phrased as case 2, with Scissors cascading into a case 2 tiebreaker.
   This can also be treated as (Slave, Master, Water, Fire, Tree) in the general framework.

Classification of RPS-like Games, N=7

5. (1₃, 1₃, 1₃, 1₃, 1₃, 1₃, 1₃) ÷ 7   ::   The "obvious" seven-way
   a > bcd, b > cde, c > def, d > efg, e > fga, f > gab, g > abc
   This case can be described with the common framework when Master rules Fire and Iron; Iron shackles Slave.)
6. (1₃, 1₃, 1₃, 1₃, 1₃, 1₃, 1₃) ÷ 7   ::   This has the same structure signature as the previous case, but is a distinct structure:
   ab > cd, cd > ef, ef > ab; bdf > g > ace; a > b, c > d, e > f
   This case can be described with the common framework when Master controls Iron and Water; Iron and Water control the Slave.
7. (1₃, 1₃, 1₃, 1₃, 1₃, 1₃, 1₃) ÷ 7   ::   This has the same structure signature as the previous case, but is a distinct structure:
   a > bce; b > cdf; c > deg; d > efa; e > fgb; f > gac; g > abd
   To express this with the common framework, we need Master defeats Iron and Earth; Earth and Iron defeat Slave, and contrary to the constant framework, Iron defeats Fire.
8. (3₃, 1₄, 1₄, 1₄, 1₂, 1₂, 1₂) ÷ 9   ::   this is similar to case 4, but now anticipatory 2nd moves are provided for both Paper and Scissors.
9. (1₃, 1₃, 1₃, 1₃, 1₃, 5₁, 5₅) ÷ 15   ::   this is case 2 with Scissors cascading into a case 3 tie-breaker.
   This case can be described with the common framework when Slave controls Fire.
10. (3₄, 3₄, 1₃, 3₂, 3₂, 1₃, 1₃) ÷ 15   ::   this is case 3 cascading into a case 2 tie-breaker.
    This case can be described with the common framework when Master enjoys Earth and Water; Iron shackles Slave.
11. (9₅, 9₁, 3₄, 3₂, 1₃, 1₃, 1₃) ÷ 27   ::   this is case 2 with Scissors cascading into a case 4 tie-breaker. (Or case 4, cascading into case 2.)
12. (1₃, 1₃, 1₃, 1₃, 1₃, 3₂, 3₄) ÷ 11   ::   Use the common description, except that Master rules Fire, and Fire burns Slave. Another way to describe case 12: it is like case 9 except that one of the group of five reverses relative to the outside two.
13. (3₄, 5₃, 1₃, 5₃, 3₂, 1₃, 1₃) ÷ 19   ::   Common framework with Fire burns Master and Slave; Earth buries Slave; Master rules Earth and Water.
14. (7₄, 1₃, 1₃, 7₂, 1₃, 3₂, 3₄) ÷ 23   ::   Common framework with Fire burns Master and Master rules Earth.
15. (5₄, 5₂, 3₃, 7₃, 3₃, 1₄, 1₂) ÷ 25   ::   Common framework with Fire burns Master and Slave; Master rules Iron, Tree and Water; Tree and Water torture Slave.
16. (7₄, 7₂, 5₃, 9₃, 5₃, 1₃, 1₃) ÷ 35   ::   Common framework but Fire burns Master and Slave; Master rules Iron and Earth; Earth buries Slave.

In my survey of N=7 cases, the seven pairs define each case, except cases 10-12 which have identical signatures. The ten mixing probability denominators, in ascending order are 7, 7, 7, 9, 11, 15, 15, 19, 23, 25, 27, 35.

Detailed Look at Case 14

Here is the Game matrix for case 14, showing the arithmetic which proves we've found the "saddle-point" strategy. To a crude approximation, game play is like the N=3 RPS with Earth outliving Fire, Fire burning Master/Slave, and Master/Slave owning Earth. Earth should be selected 30% of the time even though it loses to four out of six of the other moves.

	Fire Iron Tree Earth Water Master Slave   0 -1 -1   +1 E. outlives Fire   +1 W. quenches Fire -1 -1   7/23   +0-1-1+7+1-3-3 = 0   +1 F. melts Iron 0 -1 -1   +1 W. rusts Iron -1   +1 S. uses Iron   1/23   +7+0-1-7+1-3+3 = 0   +1 F. consumes Tree   +1 I. chops Tree 0 -1 -1 -1   +1 S. topples Tree   1/23   +7+1+0-7-1-3+3 = 0 -1   +1 I. bolsters Earth   +1 T. rends Earth 0 -1   +1 M. rules Earth   +1 S. plows Earth   X   7/23   =   -7+1+1+0-1+3+3 = 0 -1 -1   +1 T. drinks Water   +1 E. absorbs Water 0 -1   +1 S. pours Water   1/23   -7-1+1+7+0-3+3 = 0   +1 F. burns Master   +1 I. slays Master   +1 T. hangs Master -1   +1 W. drowns Master 0 -1   3/23   +7+1+1-7+1+0-3 = 0   +1 F. burns Slave -1 -1 -1 -1   +1 M. commands Slave 0   3/23   +7-1-1-7-1+3+0 = 0

The ordering of the Five Elements is based on Overcoming and Generating interactions of the Five Chinese Elements, but with the Generating arros reversed to denotes dependency. Coming up with a better group of seven moves is on my To_do List!

Classification of RPS-like Games, N=9

There are 792 cases, though only 499 distinct nonets of pairs for N=9. These are shown in a final appendix.

Classification of RPS-like Games, N=11

There are probably millions of cases; I lack the tools to explore them properly. For example, the game matrix

0-++++---+-
+0-+-+-++--
-+0--+++-++
--+0++++---
-++-0---+--
----+0+-++-
++--+-0+-+-
+---++-0+-+
+-++--+-0-+
-+-++--++0+
++-++++---0

All RPS-like Games have an odd number of plays in the optimal strategy mix

We will omit the simple inductive proof of the following Lemma: Any NxN matrix with only even integers on the diagonal and only odd integers off the diagonal will have an odd determinant if N is even and even determinant if N is odd.

Let P be the payoff matrix and s_k be the probability of choosing move k in the optimal strategy mix; and suppose that s_k > 0 for all k. (Note that if some s_k is zero, the corresponding element of P·S need not be zero.) It follows from the symmetry of the game that
      P · [s₁ s₂ s₃ ... s_N]^T = [0 0 0 ... 0]^T
This means P is singular, so has determinant zero; so P is of odd dimension by the Lemma. Q.E.D.

Appendix: Complete List of structures for N=9

As before, I omit structures where some move is dominated (has an optimal mixing probability of zero).

15 instances of (14, 14, 14, 14, 14, 14, 14, 14, 14) ÷ 9 4 instances of (34, 15, 15, 15, 15, 13, 13, 13, 13) ÷ 11 11 instances of (35, 33, 14, 14, 14, 14, 14, 14, 14) ÷ 13 1 instance of (35, 33, 16, 14, 14, 14, 14, 14, 12) ÷ 13 7 instances of (34, 34, 34, 15, 15, 15, 13, 13, 13) ÷ 15 1 instance of (36, 34, 32, 15, 15, 15, 13, 13, 13) ÷ 15 9 instances of (35, 35, 33, 33, 14, 14, 14, 14, 14) ÷ 17 1 instance of (54, 35, 33, 16, 14, 14, 14, 14, 12) ÷ 17 5 instances of (56, 52, 14, 14, 14, 14, 14, 14, 14) ÷ 17 1 instance of (53, 36, 34, 34, 15, 15, 13, 13, 13) ÷ 19 1 instance of (55, 34, 34, 32, 15, 15, 15, 13, 13) ÷ 19 3 instances of (55, 53, 34, 15, 15, 15, 13, 13, 13) ÷ 19 5 instances of (35, 35, 35, 33, 33, 33, 14, 14, 14) ÷ 21 4 instances of (54, 35, 35, 33, 33, 14, 14, 14, 14) ÷ 21 10 instances of (54, 54, 35, 33, 14, 14, 14, 14, 14) ÷ 21 1 instance of (54, 54, 35, 33, 16, 14, 14, 14, 12) ÷ 21 2 instances of (56, 52, 35, 33, 14, 14, 14, 14, 14) ÷ 21 3 instances of (77, 71, 14, 14, 14, 14, 14, 14, 14) ÷ 21 3 instances of (55, 53, 34, 34, 34, 15, 15, 13, 13) ÷ 23 2 instances of (76, 72, 34, 15, 15, 15, 13, 13, 13) ÷ 23 7 instances of (54, 54, 35, 35, 33, 33, 14, 14, 14) ÷ 25 1 instance of (56, 56, 52, 52, 14, 14, 14, 14, 14) ÷ 25 2 instances of (73, 54, 35, 35, 35, 14, 14, 14, 12) ÷ 25 1 instance of (73, 56, 54, 33, 16, 14, 14, 14, 12) ÷ 25 2 instances of (75, 54, 33, 33, 33, 16, 14, 14, 14) ÷ 25 1 instance of (75, 54, 52, 35, 16, 14, 14, 14, 12) ÷ 25 10 instances of (75, 73, 35, 33, 14, 14, 14, 14, 14) ÷ 25 7 instances of (74, 55, 53, 34, 34, 15, 15, 13, 13) ÷ 27 1 instance of (93, 36, 36, 36, 34, 32, 13, 13, 13) ÷ 27 1 instance of (95, 36, 34, 32, 32, 32, 15, 15, 15) ÷ 27 1 instance of (97, 91, 34, 15, 15, 15, 13, 13, 13) ÷ 27 5 instances of (54, 54, 54, 54, 35, 33, 14, 14, 14) ÷ 29 4 instances of (75, 73, 35, 35, 33, 33, 14, 14, 14) ÷ 29 1 instance of (75, 73, 56, 52, 14, 14, 14, 14, 14) ÷ 29 5 instances of (96, 92, 35, 33, 14, 14, 14, 14, 14) ÷ 29 6 instances of (74, 55, 53, 34, 34, 34, 34, 15, 13) ÷ 31 2 instances of (74, 74, 55, 53, 34, 15, 15, 13, 13) ÷ 31 1 instance of (117, 111, 35, 33, 14, 14, 14, 14, 14) ÷ 33 2 instances of (75, 73, 54, 35, 35, 33, 33, 14, 14) ÷ 33 9 instances of (75, 73, 54, 54, 35, 33, 14, 14, 14) ÷ 33 1 instance of (75, 73, 56, 52, 35, 33, 14, 14, 14) ÷ 33 1 instance of (94, 73, 54, 35, 35, 35, 14, 14, 12) ÷ 33 1 instance of (94, 75, 54, 33, 33, 33, 16, 14, 14) ÷ 33 1 instance of (94, 94, 35, 35, 33, 33, 14, 14, 14) ÷ 33 2 instances of (94, 94, 56, 52, 14, 14, 14, 14, 14) ÷ 33 4 instances of (96, 92, 35, 35, 33, 33, 14, 14, 14) ÷ 33 1 instance of (114, 55, 53, 36, 34, 34, 32, 15, 13) ÷ 35 5 instances of (74, 55, 55, 53, 53, 34, 34, 15, 13) ÷ 35 1 instance of (74, 74, 55, 53, 34, 34, 34, 15, 13) ÷ 35 1 instance of (93, 74, 55, 55, 34, 34, 15, 13, 13) ÷ 35 1 instance of (93, 76, 74, 53, 34, 15, 15, 13, 13) ÷ 35 1 instance of (95, 74, 53, 53, 34, 34, 15, 15, 13) ÷ 35 1 instance of (95, 74, 72, 55, 34, 15, 15, 13, 13) ÷ 35 1 instance of (115, 113, 35, 35, 33, 33, 14, 14, 14) ÷ 37 2 instances of (115, 113, 56, 52, 14, 14, 14, 14, 14) ÷ 37 5 instances of (75, 75, 73, 73, 35, 33, 14, 14, 14) ÷ 37 4 instances of (94, 75, 73, 54, 54, 14, 14, 14, 14) ÷ 37 6 instances of (94, 94, 54, 54, 35, 33, 14, 14, 14) ÷ 37 2 instances of (96, 92, 54, 54, 35, 33, 14, 14, 14) ÷ 37 10 instances of (74, 74, 74, 55, 53, 34, 34, 15, 13) ÷ 39 1 instance of (93, 76, 74, 53, 34, 34, 34, 15, 13) ÷ 39 1 instance of (95, 74, 72, 55, 34, 34, 34, 15, 13) ÷ 39 1 instance of (113, 94, 75, 54, 35, 35, 14, 14, 12) ÷ 41 1 instance of (113, 96, 54, 54, 33, 33, 33, 16, 14) ÷ 41 6 instances of (115, 113, 54, 54, 35, 33, 14, 14, 14) ÷ 41 1 instance of (115, 92, 54, 54, 35, 35, 35, 14, 12) ÷ 41 1 instance of (115, 94, 73, 54, 33, 33, 16, 14, 14) ÷ 41 1 instance of (136, 132, 35, 35, 33, 33, 14, 14, 14) ÷ 41 1 instance of (136, 132, 56, 52, 14, 14, 14, 14, 14) ÷ 41 5 instances of (94, 75, 73, 54, 54, 35, 33, 14, 14) ÷ 41 3 instances of (94, 94, 75, 73, 35, 33, 14, 14, 14) ÷ 41 2 instances of (96, 92, 75, 73, 35, 33, 14, 14, 14) ÷ 41 1 instance of (114, 93, 74, 55, 55, 34, 15, 13, 13) ÷ 43 1 instance of (114, 95, 74, 53, 53, 34, 15, 15, 13) ÷ 43 7 instances of (95, 93, 74, 55, 53, 34, 34, 15, 13) ÷ 43 3 instances of (115, 113, 75, 73, 35, 33, 14, 14, 14) ÷ 45 1 instance of (134, 134, 54, 54, 35, 33, 14, 14, 14) ÷ 45 2 instances of (136, 132, 54, 54, 35, 33, 14, 14, 14) ÷ 45 1 instance of (153, 56, 56, 56, 33, 33, 33, 33, 33) ÷ 45 1 instance of (155, 52, 52, 52, 35, 35, 35, 35, 35) ÷ 45 1 instance of (157, 151, 35, 35, 33, 33, 14, 14, 14) ÷ 45 1 instance of (157, 151, 56, 52, 14, 14, 14, 14, 14) ÷ 45 4 instances of (94, 75, 73, 54, 54, 54, 54, 14, 14) ÷ 45 1 instance of (96, 96, 92, 92, 35, 33, 14, 14, 14) ÷ 45 4 instances of (114, 114, 74, 55, 53, 34, 34, 15, 13) ÷ 47 1 instance of (114, 93, 74, 55, 55, 34, 34, 34, 13) ÷ 47 1 instance of (114, 95, 74, 53, 53, 34, 34, 34, 15) ÷ 47 1 instance of (116, 112, 74, 55, 53, 34, 34, 15, 13) ÷ 47 1 instance of (133, 95, 93, 55, 55, 36, 13, 13, 13) ÷ 47 1 instance of (135, 95, 93, 53, 53, 32, 15, 15, 15) ÷ 47 3 instances of (95, 93, 74, 74, 74, 34, 34, 15, 13) ÷ 47 1 instance of (113, 94, 75, 75, 54, 54, 33, 14, 14) ÷ 49 1 instance of (113, 94, 94, 75, 75, 33, 14, 14, 14) ÷ 49 1 instance of (113, 96, 94, 73, 54, 35, 33, 14, 14) ÷ 49 1 instance of (115, 113, 75, 73, 54, 35, 33, 14, 14) ÷ 49 1 instance of (115, 113, 96, 92, 35, 33, 14, 14, 14) ÷ 49 1 instance of (115, 94, 73, 73, 54, 54, 35, 14, 14) ÷ 49 1 instance of (115, 94, 92, 75, 54, 35, 33, 14, 14) ÷ 49 1 instance of (115, 94, 94, 73, 73, 35, 14, 14, 14) ÷ 49 1 instance of (134, 113, 75, 54, 54, 35, 35, 14, 12) ÷ 49 1 instance of (134, 115, 73, 54, 54, 33, 33, 16, 14) ÷ 49 6 instances of (134, 134, 75, 73, 35, 33, 14, 14, 14) ÷ 49 1 instance of (134, 94, 73, 56, 54, 35, 33, 33, 14) ÷ 49 1 instance of (134, 94, 75, 54, 52, 35, 35, 33, 14) ÷ 49 3 instances of (155, 153, 54, 54, 35, 33, 14, 14, 14) ÷ 49 5 instances of (94, 75, 75, 73, 73, 54, 54, 14, 14) ÷ 49 1 instance of (94, 94, 75, 73, 54, 54, 35, 33, 14) ÷ 49 2 instances of (114, 95, 93, 74, 55, 53, 34, 15, 13) ÷ 51 1 instance of (133, 114, 95, 74, 55, 34, 15, 13, 13) ÷ 51 1 instance of (135, 114, 93, 74, 53, 34, 15, 15, 13) ÷ 51 5 instances of (135, 133, 74, 55, 53, 34, 34, 15, 13) ÷ 51 1 instance of (134, 134, 96, 92, 35, 33, 14, 14, 14) ÷ 53 6 instances of (155, 153, 75, 73, 35, 33, 14, 14, 14) ÷ 53 1 instance of (174, 75, 73, 56, 52, 35, 35, 33, 33) ÷ 53 3 instances of (176, 172, 54, 54, 35, 33, 14, 14, 14) ÷ 53 9 instances of (94, 94, 94, 75, 73, 54, 54, 14, 14) ÷ 53 1 instance of (114, 114, 74, 74, 74, 55, 53, 15, 13) ÷ 55 2 instances of (114, 114, 95, 93, 74, 34, 34, 15, 13) ÷ 55 1 instance of (114, 74, 74, 74, 74, 55, 53, 34, 34) ÷ 55 1 instance of (133, 114, 76, 74, 55, 53, 34, 34, 13) ÷ 55 1 instance of (133, 114, 95, 74, 55, 34, 34, 34, 13) ÷ 55 1 instance of (133, 116, 114, 93, 34, 34, 34, 15, 13) ÷ 55 1 instance of (135, 114, 112, 95, 34, 34, 34, 15, 13) ÷ 55 1 instance of (135, 114, 74, 72, 55, 53, 34, 34, 15) ÷ 55 1 instance of (135, 114, 93, 74, 53, 34, 34, 34, 15) ÷ 55 1 instance of (154, 114, 93, 74, 55, 36, 34, 13, 13) ÷ 55 1 instance of (154, 114, 95, 74, 53, 34, 32, 15, 15) ÷ 55 1 instance of (154, 116, 112, 74, 74, 15, 15, 13, 13) ÷ 55 2 instances of (154, 154, 74, 55, 53, 34, 34, 15, 13) ÷ 55 2 instances of (156, 152, 74, 55, 53, 34, 34, 15, 13) ÷ 55 5 instances of (115, 113, 94, 75, 73, 54, 54, 14, 14) ÷ 57 2 instances of (115, 113, 94, 94, 54, 54, 35, 33, 14) ÷ 57 1 instance of (134, 113, 94, 75, 75, 54, 33, 14, 14) ÷ 57 1 instance of (134, 115, 94, 73, 73, 54, 35, 14, 14) ÷ 57 1 instance of (153, 115, 94, 56, 54, 54, 33, 33, 14) ÷ 57 1 instance of (153, 136, 94, 73, 54, 33, 33, 16, 14) ÷ 57 1 instance of (153, 96, 94, 54, 54, 54, 35, 33, 33) ÷ 57 1 instance of (155, 113, 94, 54, 54, 52, 35, 35, 14) ÷ 57 1 instance of (155, 132, 94, 75, 54, 35, 35, 14, 12) ÷ 57 3 instances of (155, 153, 96, 92, 35, 33, 14, 14, 14) ÷ 57 1 instance of (155, 94, 92, 54, 54, 54, 35, 35, 33) ÷ 57 1 instance of (174, 174, 75, 73, 35, 33, 14, 14, 14) ÷ 57 2 instances of (176, 172, 75, 73, 35, 33, 14, 14, 14) ÷ 57 1 instance of (197, 191, 54, 54, 35, 33, 14, 14, 14) ÷ 57 1 instance of (133, 114, 95, 95, 74, 53, 34, 15, 13) ÷ 59 1 instance of (133, 116, 114, 93, 55, 53, 34, 15, 13) ÷ 59 1 instance of (135, 114, 112, 95, 55, 53, 34, 15, 13) ÷ 59 1 instance of (135, 114, 93, 93, 74, 55, 34, 15, 13) ÷ 59 1 instance of (154, 114, 114, 74, 74, 34, 34, 15, 13) ÷ 59 1 instance of (154, 133, 74, 74, 55, 55, 55, 13, 13) ÷ 59 1 instance of (154, 135, 74, 74, 53, 53, 53, 15, 15) ÷ 59 4 instances of (175, 173, 74, 55, 53, 34, 34, 15, 13) ÷ 59 3 instances of (115, 113, 94, 94, 94, 54, 54, 14, 14) ÷ 61 3 instances of (134, 134, 94, 75, 73, 54, 54, 14, 14) ÷ 61 1 instance of (153, 115, 96, 73, 73, 54, 35, 33, 14) ÷ 61 1 instance of (155, 113, 92, 75, 75, 54, 35, 33, 14) ÷ 61 1 instance of (174, 115, 113, 75, 73, 35, 33, 14, 14) ÷ 61 2 instances of (174, 174, 96, 92, 35, 33, 14, 14, 14) ÷ 61 1 instance of (193, 96, 75, 73, 56, 54, 33, 33, 33) ÷ 61 3 instances of (195, 193, 75, 73, 35, 33, 14, 14, 14) ÷ 61 1 instance of (195, 92, 75, 73, 54, 52, 35, 35, 35) ÷ 61 3 instances of (114, 114, 95, 93, 74, 74, 74, 15, 13) ÷ 63 1 instance of (133, 114, 95, 74, 74, 74, 55, 34, 13) ÷ 63 1 instance of (135, 114, 93, 74, 74, 74, 53, 34, 15) ÷ 63 3 instances of (135, 133, 74, 74, 74, 55, 53, 34, 34) ÷ 63 1 instance of (154, 133, 95, 74, 74, 55, 34, 34, 13) ÷ 63 1 instance of (154, 135, 93, 74, 74, 53, 34, 34, 15) ÷ 63 1 instance of (173, 135, 114, 74, 74, 36, 34, 13, 13) ÷ 63 1 instance of (175, 133, 114, 74, 74, 34, 32, 15, 15) ÷ 63 2 instances of (196, 192, 74, 55, 53, 34, 34, 15, 13) ÷ 63 2 instances of (134, 115, 113, 94, 75, 73, 54, 14, 14) ÷ 65 1 instance of (134, 134, 115, 113, 54, 54, 35, 33, 14) ÷ 65 1 instance of (153, 134, 115, 94, 75, 54, 33, 14, 14) ÷ 65 1 instance of (153, 136, 134, 113, 54, 35, 33, 14, 14) ÷ 65 1 instance of (155, 134, 113, 94, 73, 54, 35, 14, 14) ÷ 65 1 instance of (155, 134, 132, 115, 54, 35, 33, 14, 14) ÷ 65 3 instances of (155, 153, 94, 75, 73, 54, 54, 14, 14) ÷ 65 1 instance of (174, 115, 113, 54, 54, 54, 54, 35, 33) ÷ 65 1 instance of (174, 134, 113, 75, 56, 54, 33, 33, 14) ÷ 65 1 instance of (174, 134, 115, 73, 54, 52, 35, 35, 14) ÷ 65 1 instance of (174, 136, 132, 94, 94, 14, 14, 14, 14) ÷ 65 1 instance of (174, 153, 115, 94, 54, 35, 35, 14, 12) ÷ 65 1 instance of (174, 153, 94, 75, 75, 54, 35, 14, 12) ÷ 65 1 instance of (174, 155, 113, 94, 54, 33, 33, 16, 14) ÷ 65 1 instance of (174, 155, 94, 73, 73, 54, 33, 16, 14) ÷ 65 1 instance of (174, 94, 94, 75, 73, 54, 54, 35, 33) ÷ 65 2 instances of (195, 193, 96, 92, 35, 33, 14, 14, 14) ÷ 65 3 instances of (216, 212, 75, 73, 35, 33, 14, 14, 14) ÷ 65 1 instance of (154, 133, 114, 95, 95, 53, 34, 15, 13) ÷ 67 1 instance of (154, 133, 95, 95, 74, 74, 53, 15, 13) ÷ 67 1 instance of (154, 135, 114, 93, 93, 55, 34, 15, 13) ÷ 67 1 instance of (154, 135, 93, 93, 74, 74, 55, 15, 13) ÷ 67 1 instance of (173, 135, 93, 76, 74, 55, 53, 34, 13) ÷ 67 1 instance of (175, 133, 95, 74, 72, 55, 53, 34, 15) ÷ 67 1 instance of (194, 133, 95, 95, 55, 53, 34, 32, 15) ÷ 67 1 instance of (194, 135, 93, 93, 55, 53, 36, 34, 13) ÷ 67 1 instance of (215, 213, 74, 55, 53, 34, 34, 15, 13) ÷ 67 1 instance of (134, 134, 115, 113, 75, 73, 35, 33, 14) ÷ 69 2 instances of (134, 134, 115, 113, 94, 54, 54, 14, 14) ÷ 69 1 instance of (134, 134, 94, 94, 94, 75, 73, 14, 14) ÷ 69 1 instance of (153, 136, 134, 113, 54, 54, 54, 14, 14) ÷ 69 1 instance of (155, 134, 132, 115, 54, 54, 54, 14, 14) ÷ 69 4 instances of (174, 115, 113, 75, 73, 54, 54, 35, 33) ÷ 69 1 instance of (174, 134, 134, 94, 94, 35, 33, 14, 14) ÷ 69 2 instances of (174, 174, 94, 75, 73, 54, 54, 14, 14) ÷ 69 1 instance of (176, 172, 94, 75, 73, 54, 54, 14, 14) ÷ 69 1 instance of (193, 134, 115, 75, 75, 54, 33, 33, 14) ÷ 69 1 instance of (195, 134, 113, 73, 73, 54, 35, 35, 14) ÷ 69 1 instance of (214, 113, 75, 75, 75, 54, 52, 35, 33) ÷ 69 1 instance of (214, 115, 73, 73, 73, 56, 54, 35, 33) ÷ 69 1 instance of (214, 214, 96, 92, 35, 33, 14, 14, 14) ÷ 69 1 instance of (214, 94, 92, 75, 75, 75, 35, 33, 33) ÷ 69 1 instance of (214, 96, 94, 73, 73, 73, 35, 35, 33) ÷ 69 2 instances of (216, 212, 96, 92, 35, 33, 14, 14, 14) ÷ 69 1 instance of (237, 231, 75, 73, 35, 33, 14, 14, 14) ÷ 69 1 instance of (154, 133, 114, 95, 74, 74, 55, 34, 13) ÷ 71 1 instance of (154, 135, 114, 93, 74, 74, 53, 34, 15) ÷ 71 1 instance of (173, 156, 114, 93, 74, 53, 34, 34, 15) ÷ 71 1 instance of (175, 152, 114, 95, 74, 55, 34, 34, 13) ÷ 71 1 instance of (194, 154, 133, 95, 74, 36, 34, 13, 13) ÷ 71 1 instance of (194, 154, 135, 93, 74, 34, 32, 15, 15) ÷ 71 2 instances of (236, 232, 74, 55, 53, 34, 34, 15, 13) ÷ 71 1 instance of (153, 134, 115, 115, 94, 73, 54, 14, 14) ÷ 73 1 instance of (153, 134, 115, 94, 94, 75, 54, 33, 14) ÷ 73 1 instance of (155, 134, 113, 113, 94, 75, 54, 14, 14) ÷ 73 1 instance of (155, 134, 113, 94, 94, 73, 54, 35, 14) ÷ 73 1 instance of (174, 134, 113, 94, 75, 75, 54, 33, 14) ÷ 73 1 instance of (174, 134, 115, 94, 73, 73, 54, 35, 14) ÷ 73 1 instance of (193, 174, 136, 113, 54, 35, 35, 14, 12) ÷ 73 1 instance of (195, 174, 132, 115, 54, 33, 33, 16, 14) ÷ 73 4 instances of (195, 193, 94, 75, 73, 54, 54, 14, 14) ÷ 73 1 instance of (235, 233, 96, 92, 35, 33, 14, 14, 14) ÷ 73 1 instance of (154, 135, 133, 95, 93, 74, 74, 15, 13) ÷ 75 1 instance of (154, 154, 95, 93, 74, 74, 74, 34, 34) ÷ 75 1 instance of (173, 154, 135, 114, 95, 53, 34, 15, 13) ÷ 75 1 instance of (173, 156, 154, 133, 55, 53, 34, 15, 13) ÷ 75 1 instance of (175, 154, 133, 114, 93, 55, 34, 15, 13) ÷ 75 1 instance of (175, 154, 152, 135, 55, 53, 34, 15, 13) ÷ 75 1 instance of (194, 173, 114, 95, 74, 55, 55, 13, 13) ÷ 75 1 instance of (194, 175, 114, 93, 74, 53, 53, 15, 15) ÷ 75 1 instance of (213, 154, 135, 95, 74, 55, 32, 15, 13) ÷ 75 1 instance of (213, 156, 152, 95, 95, 36, 13, 13, 13) ÷ 75 1 instance of (213, 156, 95, 93, 53, 53, 53, 36, 34) ÷ 75 1 instance of (215, 152, 95, 93, 55, 55, 55, 34, 32) ÷ 75 1 instance of (215, 154, 133, 93, 74, 53, 36, 15, 13) ÷ 75 1 instance of (215, 156, 152, 93, 93, 32, 15, 15, 15) ÷ 75 1 instance of (257, 251, 74, 55, 53, 34, 34, 15, 13) ÷ 75 3 instances of (134, 134, 115, 113, 94, 94, 94, 14, 14) ÷ 77 2 instances of (155, 153, 134, 134, 75, 73, 35, 33, 14) ÷ 77 1 instance of (174, 115, 113, 75, 75, 73, 73, 54, 54) ÷ 77

1 instance of (193, 115, 115, 94, 75, 73, 54, 54, 33) ÷ 77 1 instance of (193, 155, 113, 96, 75, 73, 54, 33, 14) ÷ 77 1 instance of (193, 155, 153, 115, 115, 33, 14, 14, 14) ÷ 77 1 instance of (195, 113, 113, 94, 75, 73, 54, 54, 35) ÷ 77 1 instance of (195, 153, 115, 92, 75, 73, 54, 35, 14) ÷ 77 1 instance of (195, 155, 153, 113, 113, 35, 14, 14, 14) ÷ 77 1 instance of (214, 153, 115, 115, 73, 54, 35, 33, 14) ÷ 77 1 instance of (214, 153, 134, 75, 75, 75, 33, 33, 14) ÷ 77 1 instance of (214, 155, 113, 113, 75, 54, 35, 33, 14) ÷ 77 1 instance of (214, 155, 134, 73, 73, 73, 35, 35, 14) ÷ 77 2 instances of (214, 214, 94, 75, 73, 54, 54, 14, 14) ÷ 77 2 instances of (216, 212, 94, 75, 73, 54, 54, 14, 14) ÷ 77 1 instance of (233, 115, 96, 94, 75, 73, 54, 33, 33) ÷ 77 1 instance of (235, 113, 94, 92, 75, 73, 54, 35, 35) ÷ 77 1 instance of (256, 252, 96, 92, 35, 33, 14, 14, 14) ÷ 77 4 instances of (154, 135, 133, 114, 114, 74, 74, 15, 13) ÷ 79 2 instances of (154, 154, 114, 114, 95, 93, 74, 15, 13) ÷ 79 1 instance of (173, 154, 114, 95, 95, 74, 74, 34, 13) ÷ 79 1 instance of (175, 154, 114, 93, 93, 74, 74, 34, 15) ÷ 79 1 instance of (194, 154, 112, 95, 95, 74, 55, 34, 13) ÷ 79 1 instance of (194, 154, 116, 93, 93, 74, 53, 34, 15) ÷ 79 1 instance of (194, 154, 133, 114, 95, 55, 34, 34, 13) ÷ 79 1 instance of (194, 154, 135, 114, 93, 53, 34, 34, 15) ÷ 79 1 instance of (194, 173, 114, 95, 95, 74, 34, 34, 13) ÷ 79 1 instance of (194, 173, 135, 114, 74, 55, 34, 34, 13) ÷ 79 1 instance of (194, 175, 114, 93, 93, 74, 34, 34, 15) ÷ 79 1 instance of (194, 175, 133, 114, 74, 53, 34, 34, 15) ÷ 79 1 instance of (174, 153, 115, 115, 94, 94, 73, 14, 14) ÷ 81 1 instance of (174, 153, 134, 115, 115, 73, 54, 14, 14) ÷ 81 1 instance of (174, 153, 134, 115, 94, 75, 54, 33, 14) ÷ 81 1 instance of (174, 155, 113, 113, 94, 94, 75, 14, 14) ÷ 81 1 instance of (174, 155, 134, 113, 113, 75, 54, 14, 14) ÷ 81 1 instance of (174, 155, 134, 113, 94, 73, 54, 35, 14) ÷ 81 1 instance of (193, 155, 134, 94, 94, 75, 54, 33, 14) ÷ 81 1 instance of (195, 153, 134, 94, 94, 73, 54, 35, 14) ÷ 81 1 instance of (214, 193, 115, 94, 75, 54, 54, 35, 12) ÷ 81 1 instance of (214, 193, 94, 94, 75, 75, 75, 14, 12) ÷ 81 1 instance of (214, 195, 113, 94, 73, 54, 54, 33, 16) ÷ 81 1 instance of (214, 195, 94, 94, 73, 73, 73, 16, 14) ÷ 81 4 instances of (235, 233, 94, 75, 73, 54, 54, 14, 14) ÷ 81 1 instance of (277, 271, 96, 92, 35, 33, 14, 14, 14) ÷ 81 1 instance of (173, 154, 135, 114, 95, 93, 55, 34, 13) ÷ 83 1 instance of (175, 154, 133, 114, 95, 93, 53, 34, 15) ÷ 83 1 instance of (194, 173, 135, 114, 95, 74, 53, 15, 13) ÷ 83 1 instance of (194, 175, 133, 114, 93, 74, 55, 15, 13) ÷ 83 1 instance of (213, 135, 114, 95, 95, 74, 53, 53, 34) ÷ 83 1 instance of (213, 175, 133, 95, 76, 74, 53, 34, 13) ÷ 83 1 instance of (215, 133, 114, 93, 93, 74, 55, 55, 34) ÷ 83 1 instance of (215, 173, 135, 93, 74, 72, 55, 34, 15) ÷ 83 2 instances of (234, 135, 133, 95, 93, 55, 53, 34, 34) ÷ 83 1 instance of (234, 173, 135, 95, 74, 55, 53, 32, 15) ÷ 83 1 instance of (234, 173, 154, 95, 95, 55, 32, 15, 13) ÷ 83 1 instance of (234, 175, 133, 93, 74, 55, 53, 36, 13) ÷ 83 1 instance of (234, 175, 154, 93, 93, 53, 36, 15, 13) ÷ 83 1 instance of (174, 155, 153, 115, 113, 54, 54, 35, 33) ÷ 85 1 instance of (174, 174, 155, 153, 75, 73, 35, 33, 14) ÷ 85 1 instance of (174, 174, 94, 94, 94, 75, 73, 54, 54) ÷ 85 1 instance of (193, 155, 115, 113, 94, 94, 75, 33, 14) ÷ 85 1 instance of (193, 176, 174, 153, 54, 54, 54, 14, 14) ÷ 85 1 instance of (195, 153, 115, 113, 94, 94, 73, 35, 14) ÷ 85 1 instance of (195, 174, 172, 155, 54, 54, 54, 14, 14) ÷ 85 1 instance of (214, 174, 113, 96, 94, 73, 54, 54, 14) ÷ 85 1 instance of (214, 174, 115, 94, 92, 75, 54, 54, 14) ÷ 85 1 instance of (233, 174, 155, 94, 75, 75, 33, 33, 14) ÷ 85 1 instance of (235, 174, 153, 94, 73, 73, 35, 35, 14) ÷ 85 2 instances of (254, 115, 113, 94, 94, 75, 73, 35, 33) ÷ 85 2 instances of (256, 252, 94, 75, 73, 54, 54, 14, 14) ÷ 85 1 instance of (194, 173, 154, 135, 74, 74, 55, 34, 13) ÷ 87 1 instance of (194, 175, 154, 133, 74, 74, 53, 34, 15) ÷ 87 2 instances of (194, 194, 135, 133, 74, 55, 53, 34, 34) ÷ 87 1 instance of (213, 175, 154, 114, 114, 55, 34, 34, 13) ÷ 87 1 instance of (213, 196, 154, 133, 74, 53, 34, 34, 15) ÷ 87 1 instance of (215, 173, 154, 114, 114, 53, 34, 34, 15) ÷ 87 1 instance of (215, 192, 154, 135, 74, 55, 34, 34, 13) ÷ 87 2 instances of (234, 175, 173, 114, 114, 34, 34, 15, 13) ÷ 87 1 instance of (174, 155, 153, 115, 113, 94, 94, 14, 14) ÷ 89 1 instance of (193, 174, 155, 134, 115, 73, 54, 14, 14) ÷ 89 1 instance of (193, 176, 174, 153, 75, 73, 54, 14, 14) ÷ 89 1 instance of (195, 174, 153, 134, 113, 75, 54, 14, 14) ÷ 89 1 instance of (195, 174, 172, 155, 75, 73, 54, 14, 14) ÷ 89 1 instance of (214, 174, 153, 115, 94, 75, 54, 33, 14) ÷ 89 1 instance of (214, 174, 155, 113, 94, 73, 54, 35, 14) ÷ 89 1 instance of (233, 214, 155, 134, 75, 54, 35, 14, 12) ÷ 89 1 instance of (235, 214, 153, 134, 73, 54, 33, 16, 14) ÷ 89 1 instance of (154, 135, 133, 114, 114, 74, 74, 74, 74) ÷ 91 3 instances of (154, 154, 114, 114, 95, 93, 74, 74, 74) ÷ 91 1 instance of (175, 173, 135, 133, 74, 74, 74, 55, 53) ÷ 91 2 instances of (175, 173, 154, 135, 133, 74, 74, 15, 13) ÷ 91 1 instance of (194, 173, 135, 135, 114, 93, 74, 15, 13) ÷ 91 1 instance of (194, 173, 135, 135, 93, 74, 55, 53, 34) ÷ 91 1 instance of (194, 173, 154, 135, 95, 93, 55, 34, 13) ÷ 91 1 instance of (194, 175, 133, 133, 114, 95, 74, 15, 13) ÷ 91 1 instance of (194, 175, 133, 133, 95, 74, 55, 53, 34) ÷ 91 1 instance of (194, 175, 154, 133, 95, 93, 53, 34, 15) ÷ 91 1 instance of (213, 135, 135, 95, 93, 74, 74, 74, 53) ÷ 91 1 instance of (213, 175, 133, 114, 95, 95, 74, 34, 13) ÷ 91 1 instance of (213, 175, 156, 133, 93, 74, 53, 34, 15) ÷ 91 1 instance of (215, 133, 133, 95, 93, 74, 74, 74, 55) ÷ 91 1 instance of (215, 173, 135, 114, 93, 93, 74, 34, 15) ÷ 91 1 instance of (215, 173, 152, 135, 95, 74, 55, 34, 13) ÷ 91 2 instances of (234, 135, 133, 95, 93, 74, 74, 55, 53) ÷ 91 1 instance of (253, 156, 135, 93, 93, 74, 55, 53, 34) ÷ 91 1 instance of (253, 194, 175, 114, 95, 55, 32, 15, 13) ÷ 91 1 instance of (255, 152, 133, 95, 95, 74, 55, 53, 34) ÷ 91 1 instance of (255, 194, 173, 114, 93, 53, 36, 15, 13) ÷ 91 4 instances of (174, 155, 153, 134, 134, 94, 94, 14, 14) ÷ 93 2 instances of (174, 174, 134, 134, 115, 113, 94, 14, 14) ÷ 93 1 instance of (174, 174, 155, 153, 94, 94, 54, 54, 14) ÷ 93 1 instance of (213, 194, 175, 154, 74, 74, 55, 34, 13) ÷ 95 1 instance of (215, 194, 173, 154, 74, 74, 53, 34, 15) ÷ 95 1 instance of (234, 154, 133, 114, 95, 95, 74, 53, 34) ÷ 95 1 instance of (234, 154, 135, 114, 93, 93, 74, 55, 34) ÷ 95 2 instances of (234, 154, 154, 95, 93, 74, 74, 55, 53) ÷ 95 1 instance of (234, 194, 173, 135, 114, 55, 34, 34, 13) ÷ 95 1 instance of (234, 194, 175, 133, 114, 53, 34, 34, 15) ÷ 95 1 instance of (234, 213, 135, 114, 95, 74, 74, 34, 13) ÷ 95 1 instance of (234, 215, 133, 114, 93, 74, 74, 34, 15) ÷ 95 1 instance of (195, 193, 115, 113, 94, 94, 94, 54, 54) ÷ 97 1 instance of (214, 193, 155, 134, 115, 94, 73, 14, 14) ÷ 97 1 instance of (214, 193, 174, 155, 94, 75, 54, 33, 14) ÷ 97 1 instance of (214, 195, 153, 134, 113, 94, 75, 14, 14) ÷ 97 1 instance of (214, 195, 174, 153, 94, 73, 54, 35, 14) ÷ 97 1 instance of (233, 195, 136, 113, 113, 94, 54, 54, 14) ÷ 97 1 instance of (235, 193, 132, 115, 115, 94, 54, 54, 14) ÷ 97 2 instances of (254, 195, 193, 134, 134, 35, 33, 14, 14) ÷ 97 1 instance of (254, 233, 134, 115, 94, 75, 75, 14, 12) ÷ 97 1 instance of (254, 235, 134, 113, 94, 73, 73, 16, 14) ÷ 97 1 instance of (315, 313, 94, 75, 73, 54, 54, 14, 14) ÷ 97 2 instances of (234, 175, 173, 135, 133, 55, 53, 34, 34) ÷ 99 1 instance of (253, 234, 175, 154, 74, 55, 55, 13, 13) ÷ 99 1 instance of (255, 234, 173, 154, 74, 53, 53, 15, 15) ÷ 99 1 instance of (174, 174, 134, 134, 94, 94, 94, 75, 73) ÷ 101 2 instances of (195, 193, 174, 174, 94, 94, 54, 54, 14) ÷ 101 1 instance of (233, 195, 153, 115, 115, 94, 94, 33, 14) ÷ 101 1 instance of (235, 193, 155, 113, 113, 94, 94, 35, 14) ÷ 101 2 instances of (336, 332, 94, 75, 73, 54, 54, 14, 14) ÷ 101 1 instance of (194, 194, 154, 135, 133, 114, 114, 15, 13) ÷ 103 1 instance of (234, 213, 154, 135, 114, 95, 74, 34, 13) ÷ 103 1 instance of (234, 215, 154, 133, 114, 93, 74, 34, 15) ÷ 103 1 instance of (253, 234, 175, 154, 95, 74, 34, 34, 13) ÷ 103 1 instance of (253, 234, 196, 173, 74, 55, 34, 34, 13) ÷ 103 1 instance of (255, 234, 173, 154, 93, 74, 34, 34, 15) ÷ 103 1 instance of (255, 234, 192, 175, 74, 53, 34, 34, 15) ÷ 103 1 instance of (314, 175, 173, 95, 93, 76, 72, 34, 34) ÷ 103 2 instances of (195, 193, 174, 155, 153, 94, 94, 14, 14) ÷ 105 1 instance of (214, 193, 155, 155, 134, 113, 94, 14, 14) ÷ 105 1 instance of (214, 195, 153, 153, 134, 115, 94, 14, 14) ÷ 105 1 instance of (214, 214, 174, 115, 113, 75, 73, 54, 54) ÷ 105 1 instance of (233, 214, 195, 174, 94, 75, 54, 33, 14) ÷ 105 1 instance of (233, 216, 214, 193, 75, 73, 54, 14, 14) ÷ 105 1 instance of (235, 214, 193, 174, 94, 73, 54, 35, 14) ÷ 105 1 instance of (235, 214, 212, 195, 75, 73, 54, 14, 14) ÷ 105 2 instances of (235, 233, 174, 115, 113, 75, 73, 35, 33) ÷ 105 2 instances of (254, 195, 193, 115, 113, 75, 73, 35, 33) ÷ 105 1 instance of (273, 216, 155, 153, 73, 73, 73, 35, 35) ÷ 105 1 instance of (273, 216, 212, 155, 155, 33, 14, 14, 14) ÷ 105 1 instance of (273, 216, 214, 153, 54, 54, 54, 35, 33) ÷ 105 1 instance of (275, 212, 155, 153, 75, 75, 75, 33, 33) ÷ 105 1 instance of (275, 214, 212, 155, 54, 54, 54, 35, 33) ÷ 105 1 instance of (275, 216, 212, 153, 153, 35, 14, 14, 14) ÷ 105 1 instance of (357, 351, 94, 75, 73, 54, 54, 14, 14) ÷ 105 1 instance of (215, 213, 175, 173, 154, 74, 74, 15, 13) ÷ 107 1 instance of (234, 213, 175, 154, 135, 93, 74, 15, 13) ÷ 107 1 instance of (234, 213, 194, 175, 95, 93, 55, 34, 13) ÷ 107 1 instance of (234, 215, 173, 154, 133, 95, 74, 15, 13) ÷ 107 1 instance of (234, 215, 194, 173, 95, 93, 53, 34, 15) ÷ 107 1 instance of (253, 215, 173, 135, 114, 95, 74, 34, 13) ÷ 107 1 instance of (255, 213, 175, 133, 114, 93, 74, 34, 15) ÷ 107 1 instance of (214, 214, 195, 193, 94, 94, 54, 54, 14) ÷ 109 1 instance of (194, 194, 175, 173, 154, 114, 114, 15, 13) ÷ 111 1 instance of (234, 194, 173, 154, 135, 114, 74, 55, 13) ÷ 111 1 instance of (234, 194, 175, 154, 133, 114, 74, 53, 15) ÷ 111 1 instance of (314, 215, 213, 135, 133, 55, 53, 15, 13) ÷ 111 1 instance of (214, 214, 195, 193, 115, 113, 54, 54, 14) ÷ 113 2 instances of (254, 174, 174, 115, 113, 94, 94, 75, 73) ÷ 113 1 instance of (253, 234, 215, 194, 95, 93, 55, 34, 13) ÷ 115 1 instance of (255, 234, 213, 194, 95, 93, 53, 34, 15) ÷ 115 1 instance of (314, 154, 154, 135, 133, 95, 93, 55, 53) ÷ 115 1 instance of (314, 236, 232, 154, 154, 34, 34, 15, 13) ÷ 115 1 instance of (214, 214, 174, 155, 153, 134, 134, 14, 14) ÷ 117 2 instances of (254, 214, 155, 153, 134, 134, 94, 54, 14) ÷ 117 1 instance of (334, 233, 195, 155, 113, 75, 52, 35, 14) ÷ 117 1 instance of (334, 235, 193, 153, 115, 73, 56, 33, 14) ÷ 117 1 instance of (194, 194, 175, 173, 135, 133, 74, 74, 74) ÷ 119 1 instance of (213, 175, 175, 154, 154, 133, 74, 74, 74) ÷ 119 1 instance of (213, 194, 175, 154, 135, 114, 93, 74, 74) ÷ 119 1 instance of (215, 173, 173, 154, 154, 135, 74, 74, 74) ÷ 119 1 instance of (215, 194, 173, 154, 133, 114, 95, 74, 74) ÷ 119 1 instance of (215, 213, 154, 135, 133, 114, 114, 74, 74) ÷ 119 1 instance of (234, 173, 154, 154, 135, 135, 93, 74, 74) ÷ 119 1 instance of (234, 175, 154, 154, 133, 133, 95, 74, 74) ÷ 119 1 instance of (274, 253, 194, 175, 114, 95, 74, 34, 13) ÷ 119 1 instance of (274, 255, 194, 173, 114, 93, 74, 34, 15) ÷ 119 1 instance of (333, 234, 175, 175, 95, 93, 55, 53, 13) ÷ 119 1 instance of (335, 234, 173, 173, 95, 93, 55, 53, 15) ÷ 119 1 instance of (354, 213, 175, 114, 95, 95, 74, 72, 34) ÷ 119 1 instance of (354, 215, 173, 114, 93, 93, 76, 74, 34) ÷ 119 1 instance of (235, 233, 195, 193, 174, 94, 94, 14, 14) ÷ 121 2 instances of (235, 233, 214, 214, 115, 113, 54, 54, 14) ÷ 121 1 instance of (254, 233, 195, 174, 155, 113, 94, 14, 14) ÷ 121 1 instance of (254, 235, 193, 174, 153, 115, 94, 14, 14) ÷ 121 2 instances of (234, 194, 194, 154, 154, 95, 93, 74, 74) ÷ 123 2 instances of (234, 215, 213, 175, 173, 114, 114, 15, 13) ÷ 123 2 instances of (234, 234, 154, 154, 114, 114, 95, 93, 74) ÷ 123 1 instance of (253, 215, 215, 194, 133, 114, 74, 53, 15) ÷ 123 1 instance of (255, 213, 213, 194, 135, 114, 74, 55, 13) ÷ 123 1 instance of (214, 214, 195, 193, 174, 134, 134, 14, 14) ÷ 125 1 instance of (334, 195, 193, 155, 153, 75, 73, 54, 54) ÷ 125 1 instance of (334, 256, 252, 174, 174, 35, 33, 14, 14) ÷ 125 1 instance of (353, 254, 195, 155, 115, 75, 73, 52, 14) ÷ 125 1 instance of (355, 254, 193, 153, 113, 75, 73, 56, 14) ÷ 125 1 instance of (254, 254, 235, 233, 115, 113, 54, 54, 14) ÷ 129 1 instance of (273, 235, 195, 174, 153, 134, 94, 54, 14) ÷ 129 1 instance of (275, 233, 193, 174, 155, 134, 94, 54, 14) ÷ 129 1 instance of (334, 193, 174, 155, 134, 115, 94, 73, 54) ÷ 129 1 instance of (334, 195, 174, 153, 134, 113, 94, 75, 54) ÷ 129 1 instance of (334, 195, 193, 134, 134, 94, 94, 75, 73) ÷ 129 1 instance of (334, 313, 195, 174, 115, 94, 54, 35, 12) ÷ 129 1 instance of (334, 315, 193, 174, 113, 94, 54, 33, 16) ÷ 129 2 instances of (254, 214, 214, 174, 174, 94, 94, 75, 73) ÷ 133 1 instance of (313, 235, 214, 195, 153, 94, 75, 54, 33) ÷ 133 1 instance of (315, 233, 214, 193, 155, 94, 73, 54, 35) ÷ 133 1 instance of (334, 235, 233, 195, 193, 54, 54, 35, 33) ÷ 133 1 instance of (353, 214, 195, 155, 155, 94, 73, 73, 54) ÷ 133 1 instance of (355, 214, 193, 153, 153, 94, 75, 75, 54) ÷ 133 2 instances of (254, 235, 233, 195, 193, 134, 134, 14, 14) ÷ 137 1 instance of (353, 334, 235, 214, 94, 75, 75, 14, 12) ÷ 137 1 instance of (355, 334, 233, 214, 94, 73, 73, 16, 14) ÷ 137 1 instance of (314, 194, 194, 175, 173, 114, 114, 74, 74) ÷ 139 1 instance of (333, 255, 234, 175, 133, 114, 95, 53, 34) ÷ 139 1 instance of (335, 253, 234, 173, 135, 114, 93, 55, 34) ÷ 139 1 instance of (354, 253, 215, 215, 173, 74, 55, 53, 34) ÷ 139 1 instance of (354, 255, 213, 213, 175, 74, 55, 53, 34) ÷ 139 1 instance of (254, 254, 174, 155, 153, 134, 134, 94, 94) ÷ 141 1 instance of (314, 234, 234, 135, 133, 114, 114, 95, 93) ÷ 143 1 instance of (333, 314, 255, 234, 114, 95, 74, 34, 13) ÷ 143 1 instance of (335, 314, 253, 234, 114, 93, 74, 34, 15) ÷ 143 1 instance of (354, 333, 215, 194, 135, 114, 74, 34, 13) ÷ 143 1 instance of (354, 335, 213, 194, 133, 114, 74, 34, 15) ÷ 143 2 instances of (234, 215, 213, 194, 194, 154, 154, 74, 74) ÷ 147 1 instance of (234, 234, 194, 194, 175, 173, 154, 74, 74) ÷ 147 1 instance of (355, 353, 235, 233, 174, 75, 73, 35, 33) ÷ 153 1 instance of (334, 235, 233, 214, 214, 134, 134, 75, 73) ÷ 161 1 instance of (334, 254, 233, 214, 195, 134, 115, 94, 73) ÷ 161 1 instance of (334, 254, 235, 214, 193, 134, 113, 94, 75) ÷ 161 1 instance of (353, 235, 214, 214, 195, 134, 134, 94, 73) ÷ 161 1 instance of (355, 233, 214, 214, 193, 134, 134, 94, 75) ÷ 161 1 instance of (314, 255, 253, 215, 213, 194, 194, 74, 74) ÷ 175 1 instance of (354, 354, 314, 215, 213, 114, 114, 95, 93) ÷ 183 Click to return to my Home Page.