Insertion: place the two kings on the board so that White to play can mate in one. 1.Kxf2# *
Series helpmate in four 1...h1T 2.-- Kh2 3.-- Tg1 4.-- Kh1 5.Th4# *
Series helpmate in four (twin) 1...g1S 2.-- Sf3 3.-- Sh4 4.-- Sg2 5.Tf1# *
Series helpmate in eight. 1...La6 2.-- Td4 3.-- Ta2 4.-- Sf2 5.-- Sd1 6.-- Le3 7.-- Lc1 8.-- Sb2 9.Txc1# *
Series helpmate in 21 moves 1...a4 2.-- a3 3.-- a2 4.-- a1T 5.-- Tg1 6.-- Txg4 7.-- Tg5 8.-- Tb5 9.-- g5 10.-- g4 11.-- g3 12.-- g2 13.-- g1D 14.-- Dxe3 15.-- Dxc3 16.-- Da5 17.-- c3 18.-- c2 19.-- c1L 20.-- Lf4 21.-- Lb8 22.axb8S# *
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