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The number is originally infinite, made finite by the limitation.

No, it's still infinite. Infinity minus any finite number is the same infinity you started with. You can't make it smaller by subtracting finite numbers from it.

the number of possible solutions is limited by the number of people in the world. Not infinity.

1 person can think of ∞ solutions

if you thought of one solution every second for your entire 100 year life it would still not be infinity. If would just be a large number. 3.1E9 * 7E12 = 2.1e22 is still < infinity