Re: combinatoric card problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg25854] Re: combinatoric card problem*From*: Will Self <wself at msubillings.edu>*Date*: Wed, 1 Nov 2000 01:25:39 -0500 (EST)*References*: <8tdrsn$61d@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <8tdrsn$61d at smc.vnet.net>, "pw" <pewei at nospam.algonet.se> wrote: > In China they often play this card game: > put four card on a table and try, as fast as possible, to arrive to the > result 24 using only addtion subtraction multiplication and division. > > ex. the cards: { hearts_6 ,hearts_7 ,clove_8 ,spades_king } gives the > numbers: > > {6,7,8,12} > > and 12*(6+8)/7=24 > > Is there some way to do determine how to do this with mathematica, or maybe > there is some way to determine if a certain quadruple can make the required > result? > > Peter W Are parentheses allowed in the Chinese game? I would think if it's a folk game, the operations would have to be applied in order, like the old-fashioned hand calculators. Anyway, assuming you do allow parentheses, you can solve this in Mathematica by just trying every possibility. I wouldn't know of any other way. --------------------------------------------------------------- (* Define a reverse division and subtraction: *) divR[x_, y_] := Divide[y, x] subR[x_, y_] := Subtract[y, x] (* There are now six operations but we only use three in any particular try. *) (* Define the function f to show how to apply the operations to numbers: *) f[operations[h1_, h2_, h3_], numbers[n1_, n2_, n3_, n4_]] := h1[n1, h2[n2, h3[n3, n4]]] (* Now just try every possible combination. Don't use a slow computer. *) cardSolution[{a_, b_, c_, d_}] := Select[Flatten[Outer[use, Flatten[Outer[operations, Sequence @@ Table[{Plus, Subtract, subR, Times, Divide, divR}, {3}]]], numbers @@ # & /@ Permutations[{a, b, c, d}]]], (# /. use -> f) == 24 &] (* Try it: *) cardSolution[{6, 7, 8, 12}] // ColumnForm ---------------------------------------------------------------- Will Self Sent via Deja.com http://www.deja.com/ Before you buy.