**Inventory012: Another variant of nim **(proposed by Stephen
C. Locke, 11/14/01).

This problem is based on my misreading of Problem 714 of CMJ.

Two players P_0 and P_1, play Nim with one extra feature. Before P_i
moves, P_{1-i} specifies exactly one Nim-pile, H_j, and one integer, m.
P_i is then forbidden from taking exactly m from the pile H_j (although
he would be allowed to take m from another pile the same size as H_j, if
one exists). Determine a winning strategy for this game.

The version in the journal allows (as I now read it) the blocker to
list an integer for each pile, rather than for just one. I cannot estimate
the difficulty of this question. It might be no harder than the regular
Nim strategy, or it might be completely very sporadic. (I assume that the
one in [1] is barely more difficult than regular nim.)

It might make a good problem for a high school student to spend a semester
on in preparation for a science fair.

**Discussion.**

**Bibliography. [1] Problem 714, College Math. Journal,
32 (2001) 382.**

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