Talk:4-rings or 4-squares puzzle: Difference between revisions
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X must have a minimum value of d when b,c,e,f=0 and a maximum value of 18 when a,b=9.
For d=0..9 I generate something Pascal's Triangle like for the count Z of solutions:
d=9 Z9 = 10 ->
d=8 Z8 = 38 -> 2*1 +
d=7 Z7 = 82 -> 2*1 + 2*2*2 + 8*3*3
d=6 Z6 =140 -> 2*1 + 2*2*2 + 2*3*3 + 7*4*4
d=5 Z5 =210 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 6*5*52
d=4 Z4 =290 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 2*5*5 + 5*6*6
d=3 Z3 =378 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 2*5*5 + 2*6*6 + 4*7*7
d=2 Z2 =472 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 2*5*5 + 2*6*6 + 2*7*7 + 3*8*8
d=1 Z1 =570 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 2*5*5 + 2*6*6 + 2*7*7 + 2*8*8 + 2*9*9
d=0 Z0 =670 -> 2*1 + 2*2*2 + 2*3*3 + 2*4*4 + 2*5*5 + 2*6*6 + 2*7*7 + 2*8*8 + 2*9*9 + 1*10*10
Sum of Z0 through Z9 is 2860
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--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 17:49, 25 January 2017 (UTC)
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