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.

I partially brute forced this one, I started by going thru all the possible 1,2, and 3 button combinations recording the first sequence for each of 1 thru 20 thus recording the shortest possible sequence for that particular number.  After some of the 3 button combinations I began to notice what some of the underlying structure is but I don't think I have all of the functionality quite yet, but I got enough to find the shortest sequence for each of 1 thru 20 and they are:
1 A
2 AAAB
3 B
4 AB
5 ABA
6 AAAC
7 C
8 AC
9 ACA
10 BC
11 ABC
12 ABAC
13 BCB
14 CBAB
15 CAC
16 ACAC
17 CBC
18 CBCA
19 ABCAC
20 BCBC
from what I can see pushing each button adds its value to the current value in the display with 1 exception, if you press a button twice in a row then the second time it instead subtracts twice its value.  For instance pressing A gives 1, pressing AA gives 1-2*1=-1, and pressing it a 3rd time goes back to adding its value thus AAA gives 1-2*1+1=0 and pressing a button continuosly repeats this pattern.

Posted by Daniel on 2009-12-01 13:22:33