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# Ponder This

Welcome to our monthly puzzles.
You are cordially invited to match wits with some of the best minds in IBM Research.

## July 2022 - Solution

July 2022 Challenge

July 2022 Solution:

One solution, given by Kevin Bauer, is:

[
(855661, 1395050, 1402703, 1575981, 2956165, 4346904, 5516627, 5693538, 6096226, 7359806),
(855661, 1395050, 1402703, 1575981, 2560462, 4346904, 5693538, 5912330, 6096226, 7359806),
(183896, 855661, 1395050, 1402703, 1575981, 2560462, 4346904, 5693538, 7359806, 11824660),
(183896, 855661, 1346634, 1395050, 1402703, 1575981, 2560462, 7359806, 8693808, 11824660),
(367792, 855661, 1346634, 1395050, 1402703, 1575981, 2560462, 7359806, 8509912, 11824660),
(367792, 855661, 1346634, 1402703, 1575981, 2560462, 2790100, 7114862, 7359806, 11824660),
(367792, 855661, 1346634, 1387397, 1575981, 2560462, 2805406, 7114862, 7359806, 11824660),
(244944, 367792, 855661, 1346634, 1387397, 1575981, 2560462, 2805406,11824660, 14229724),
(244944, 244944, 367792, 855661, 1346634, 1387397, 1575981, 5120924, 11824660, 14229724),
(0, 367792, 489888, 855661, 1346634, 1387397, 1575981, 5120924, 11824660, 14229724)
]
For the bonus part, in order to be able to reach 0 in all cells but one, the sum of all cells must be a power of 2; any change to the cells that ensures it will work. A simple solution given by John Tromp relies on the following
(1576000, 1576000, 1576000, 1576000, 3152000, 4728000, 6304000, 6304000, 6304000, 17336000)