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MathGroup Archive 2006

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Re: Arithmetic Puzzle (so simple it's hard)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71321] Re: Arithmetic Puzzle (so simple it's hard)
  • From: Scott Hemphill <hemphill at hemphills.net>
  • Date: Wed, 15 Nov 2006 06:43:11 -0500 (EST)
  • References: <ejc4pv$6nf$1@smc.vnet.net>
  • Reply-to: hemphill at alumni.caltech.edu

Bruce Colletti <vze269bv at verizon.net> writes:

> How would this problem be solved in Mathematica?
> 
> BUT * ASK = FEAST, where each letter is a 1-digit number, no two letters may stand for the same number, and the letters are in {0,1,2,4,5,6,7,9}.

Represent the possible solutions by a list x, where

  x[[1]] is the value for "A"
  x[[2]] is the value for "B"
  x[[3]] is the value for "E"
  x[[4]] is the value for "F"
  x[[5]] is the value for "K"
  x[[6]] is the value for "S"
  x[[7]] is the value for "T"
  x[[8]] is the value for "U"

A function which tests whether the list x satisfies the condition
BUT * ASK = FEAST looks like:

In[1]:= test[x_] := {100, 10, 1} . {x[[2]], x[[8]], x[[7]]}*
        {100, 10, 1} . {x[[1]], x[[6]], x[[5]]} == {10000, 1000, 100, 10, 1} .
        {x[[4]], x[[3]], x[[1]], x[[6]], x[[7]]}

This function returns True if the condition is satisfied, otherwise False.

To solve the problem just select the permutations of {0,1,2,4,5,6,7,9} which
satisfy the test:

In[2]:= Select[Permutations[{0,1,2,4,5,6,7,9}], test]

Out[2]= {{1, 6, 5, 9, 2, 4, 0, 7}, {4, 0, 7, 2, 1, 9, 6, 5}}

You might want to exclude the second solution because it sets "B" to 0.

In[3]:= Select[%, #[[2]]!=0&]

Out[3]= {{1, 6, 5, 9, 2, 4, 0, 7}}

This list corresponds to 670 * 142 = 95140.

Scott
-- 
Scott Hemphill	hemphill at alumni.caltech.edu
"This isn't flying.  This is falling, with style."  -- Buzz Lightyear


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