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The problem

White must start with 1. e4. On move 5, white must underpromote to a knight for checkmate.

IM Miodrag Perunovic told me recently that he sent this problem to Garry Kasparov for his students a few decades ago, but none of them could figure it out. In fact, Garry ended up asking Mio directly for the solution after he himself couldn't figure it out within 24 hours! Can anyone here figure it out?

My ideas

I spent several hours myself on the problem and could not figure it out. However, here are two example ideas of how I can visualize possible underpromotions leading to checkmate. Even though neither of them solve the original problem, maybe they'll help inspire someone to actually find the solution.

[FEN ""]
1. e4 e5 2. Ke2 d5 3. Kf3 dxe4+ 4. Kg3 e3 5. Qf3 e2 6. a3 exf1=N#

There are several issues here, but a crucial problem is that black needs to move both the e and d pawns in order to create the mating net resulting in a mate-in-6.

[FEN ""]
1. d3 e5 2. b3 e4 3. Kd2 exd3 4. Kc3 dxe2 5. Kb2 exd1=N#

The issue here is that black is the one mating white on move 5 and nothing has to do with 1. e4.

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    The common story is that Kasparov failed to solve the problem "White plays 1.e4 and Black plays 5...NxR, what happened?". I don't think "White promotes to knight on move 5 and mates" is a solvable problem (even without requiring 1.e4), because "Black promotes to knight on move 5 and mates" is another famous problem (you gave its solution, with 5.Kb2 exd1N#) and we cannot spare a tempo. Could it be that Perunovic doesn't remember well, or that you misunderstood the problem ?
    – Evargalo
    Jan 13 at 19:42
  • @Evargalo Hmmm I suppose it's possible he misremembered the original problem. I did show him both of these "solutions" though, and he said that they were pretty creative but not the solution, so now your comment leaves me with even more questions! Jan 13 at 19:46

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