5.AE. REVERSING CUPS
New section. There are several versions of this and they usually involve parity. The basic move is to reverse two of the cups. The classic problem seems to be to start with UDU and produce DDD in three moves. A trick version is to demonstrate this several times to someone and then leave him to start from DUD. Another easy problem is to leave three cups as they were after three moves. This is equivalent to a 3 x 3 array with an even number in each row and column -- see 6.AO.2. These problems must be much older than I have, but the following are the only examples I have yet noted.
Anonymous. Social Entertainer and Tricks (thus on spine, but running title inside is New Book of Tricks). Apparently a compilation with advertisements for Johnson Smith (Detroit, Michigan) products, c1890?. P. 38a: Bottoms up. Given UDU, produce DDD in three moves.
Young World. c1960. P. 39: Water switch. Full and empty glasses: FFFEEE. Make them alternately full and empty in one move.
Putnam. Puzzle Fun. 1978.
No. 3: Tea for three, pp. 1 & 25. Cups given as UDU. Produce DDD in three moves.
No. 16: Glass alignment, pp. 5 & 28. Six cups arranged UUUDDD. Produce an alternating row. He gets UDUDUD in three moves. I can get DUDUDU in four moves.
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