Re: combinatoric card problem
- To: mathgroup at smc.vnet.net
- Subject: [mg25891] Re: combinatoric card problem
- From: Will Self <wself at msubillings.edu>
- Date: Tue, 7 Nov 2000 02:56:01 -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
You can do it by brute force. Paste the following into Mathematica.
---------------------------------------------------------
(* Trying to use four numbers and the four arithmetic operations to get
24. For example, (6 + 8)/7*12 = 24. *)
(*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]]]
(*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
------------------------------------------------------------
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