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Posers and Puzzles

Posers and Puzzles

  1. 27 Jun '04 22:32
    Five of these pseudo-numbers interact together to give the number 1 as a solution.

    Which five numbers and in which order?

    +19 x9 +29 x7 -999
    -94 +173 +65 -236 x8
    +122 x5 x212 +577 -567
    +190 x6 x4 -435 x22
    x13 -87 x12 -172 +177

    -Ray.
  2. 10 Jul '04 16:04
    There are 3 solutions with no multiplication:
    -236 -94 +19 +122 +190
    -236 -87 +29 +122 +173
    -172 -94 +29 +65 +173

    There is 1 solution involving a repeated multiplication added to two numbers:
    -435 -172 +19 x4 x8

    There is 1 solution involving a repeated multiplication added to a product:
    -567 x9 +29 x8 x22

    There are 8 solutions involving two products:
    -999 +65 x6 +122 x5
    -567 -94 x5 +173 x6
    -435 x8 +19 +577 x6
    -236 -172 x12 +177 x13
    -236 -87 x4 +65 x9
    -172 x7 +65 +190 x6
    -172 x8 -87 +122 x12
    -172 x9 +29 +190 x8

    There are 11 solutions involving one product:
    -999 -435 +19 +177 x8
    -999 -236 -94 +190 x7
    -567 -435 -236 +177 x7
    -567 -236 -172 +122 x8
    -567 +19 +29 +65 x8
    -435 -236 +19 x5 +577
    -236 -172 +19 +65 x6
    -236 -172 +29 x8 +177
    -236 -94 -87 +19 x22
    -172 -94 +29 x5 +122
    -94 x4 +65 +122 +190

    Altogether there are 24 different solutions.
  3. 10 Jul '04 16:46
    Please, tell me that you wrote a neat little computer program to generate these solutions by brute force, and that you did not spend time doing them by hand.

    -Ray.
  4. 11 Jul '04 11:42
    I used an Excel macro
  5. 11 Jul '04 20:24
    Originally posted by garethn
    I used an Excel macro
    Good work.

    It pains me to imagine you sitting under a low-wattage light, in the middle of the night, with pen and paper, writing out every permutation and determining whether it results in 1.

    -Ray.