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 Disagreeable Calculator (Posted on 2009-12-01)
This very Disagreeable calculator will produce the integers 1 through 20.

aaaaaa1aaa A
aaaaaa2aaa AA
aaaaaa3aaa AAA ...

Please press "Clear" to start2, and at any time to reset the display.

Note
1. The example response table is clearly not correct!
2. If you invoked a time/date stamp please press "Clear".
3. Use your keying as efficiently as possible.

 See The Solution Submitted by brianjn Rating: 1.0000 (1 votes)

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 solution | Comment 3 of 5 |

Experiment shows that the first press of a given button adds the amount on its face to the total. The second press in succession subtracts twice the face amount from the total, so that two presses in succession on net subtract the face amount from the total, as can be seen for example in a sequence of presses of 1 from the cleared position:

1,-1,0,-2,-1,-3,-2,-4,...

In accordance with the instructions, label A is used for the 1 key, B for the 3 key and C for the 7 key:

`to get                  press1                       A2                       BAA3                       B4                       BA5                       CBBA  (7-3+1) but ABA is shorter (1+3+1)6                       CAA   (7-1)7                       C8                       CA9                       CBAA  (7+3-1) but ACA is shorter (1+7+1)10                      CA11                      CBA12                      ABCA  (1+3+7+1)13                      CAAC  (7-1+7)14                      CBAB  (7+3+1+3)15                      CAC16                      CACA17                      CBC18                      CBCA19                      CACAB20                      CBCB`

In many of these order doesn't matter, such as CBA = 11 can permute the CBA into any of its 6 permutations. Only successive presses of the same key must be kept together, and separate presses can't be placed together.

 Posted by Charlie on 2009-12-01 16:27:47

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