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I don’t think this was difficult at all, though, I have played about a 1000 mates with R+K vs K over the years, so the very first thought I had was offereing black the opportunity to capture a rook at d1 so that white could play Kxc3 and mate on the next move. If black declines, the offer, it is still mate in 3:
1. Rd1! Kb2 (Kd1 2.Kc3 Kc1 3.Re1#)
2. Rc3 Ka2
3. Rc2#
Wow I never thought it was difficult. I got the solution in 5 seconds first time ever to take me that short amount of time when it mentioned difficult challenge.
1. Rd1, Kxd1
2. Kxd1, Kxc3
3. Kc1, Re1#
1. …….. Kb2
2. Rxc3, Ka2
3. Rc2#
Rd1!!
1.Rd1…
a) 1…Kxd1 2. Kxc3 Kc1 3. Re1#
b) 1…Kb2 2. Rxc3 Ka2 3. Rc2#
1. Rd1
A. 1…K:d1 2. K:c3 Kc1 3. Re1#
B. 1…Kb2 2. R:d3 Ka2 3. Rc2#
1.Rd1 Kxd1
(1…Kb2 2.Rxc3 Ka2 3.Rc2#)
2.Kxc3 Kc1 3.Re1#