Puzzle time - subtracting around the corner
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wrote on 10 Jul 2022, 11:34 last edited by
Write down four integers between 0 and 100, in a horizontal line. Now perform the following operation: Compute the (absolute) difference between the first and second, and write it under the first; then write the difference between the second and third under the second; then the difference between the third and the fourth, under the third; finally, the difference between the fourth and the first, under the fourth. You now have a new line of four integers, still between 0 and 100.
Example: If you start with 41 22 6 93, your new line will be 19 16 87 52.
If you repeat this operation you will eventually reach 0 0 0 0. (Why? Note that with five numbers instead of four, this might never happen.) Your score is the number of operations it takes to reach this sorry state.
For the example above, you end up with
41 22 6 93
19 16 87 52
3 71 35 33
68 36 2 30
32 34 28 38
2 6 10 6
4 4 4 4
0 0 0 0for a score of 7 (pretty crummy).
What's the highest score you can achieve?
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wrote on 10 Jul 2022, 11:55 last edited by Klaus 7 Oct 2022, 12:22
Hm, doesn't sound so terribly hard.
I can improve the lower bound to 13:
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wrote on 10 Jul 2022, 12:29 last edited by Klaus 7 Oct 2022, 12:36
As for why you eventually reach 0 0 0 0:
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wrote on 13 Jul 2022, 05:16 last edited by
HINT: What's happening to parity as you perform your operations?
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wrote on 13 Jul 2022, 06:06 last edited by
Ah, I see.
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