This very Disagreeable calculator will produce the integers 1 through 20.

Tabulate your response ¹, eg:
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.

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                  press
1                       A
2                       BAA
3                       B
4                       BA
5                       CBBA  (7-3+1) but ABA is shorter (1+3+1)
6                       CAA   (7-1)
7                       C
8                       CA
9                       CBAA  (7+3-1) but ACA is shorter (1+7+1)
10                      CA
11                      CBA
12                      ABCA  (1+3+7+1)
13                      CAAC  (7-1+7)
14                      CBAB  (7+3+1+3)
15                      CAC
16                      CACA
17                      CBC
18                      CBCA
19                      CACAB
20                      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