[Timothee]

I'd think of the thought process a bit differently than lclarkmichalek, though of course with the same result.

To get close to 952, you can quickly think of 106x9. 106 is easy to obtain and you have a 3. You can get another 3 from 75/25. You're now at 954 with only a 50 left. If you could divide by 25, that would give you the 2 you're missing but you already used the 25, unless you were to divide later. So instead of doing 106x3x(75/25), you do (106x3x75-50)/25.

He could have certainly thought of it another way but based on how players typically play that game, that would be a somewhat logical progression.

[judofyr]

Another way to think about it:

He had the numbers 100, 3, 6, 25, 50, 75. 25, 50 and 75 are big and difficult to work with, but 50/25=2 and 75/25=3 are far easier. He could either do it right away, but that gives him either (2 and 75) or (3 and 25) and there's still a large number. (75x ± 50y)/25 on the other hand equals (3x ± 2y) and he's down to nice small numbers.

[malvim]

I was wondering how he thought of that. Even though we don't know, this explanation is beautiful and makes a lot of sense. Thanks!