Sources page biographical material

6.BE. REVERSE A TRIANGULAR ARRAY OF TEN CIRCLES
One has a triangle of ten coins with four on an edge. Reverse its direction by moving only three coins. New section -- I'm surprised not to have seen older examples.
Sid G. Hedges. More Indoor and Community Games. Methuen, London, 1937. The triangle trick, p. 54. Uses peas, buttons or nuts.

M. Adams. Puzzle Book. 1939. Prob. B.34: Pitching camp, pp. 66 & 103. Array of tents.

Evelyn August. The Black-Out Book. Op. cit. in 5.X.1. 1939. The General inspects the balloons, pp. 106 & 214. Array of 10 barrage balloons.

Leopold. At Ease! 1943. 1, 2, 3 -- shift!, pp. 20 & 198. Thanks to Heinrich Hemme for the lead to this.

Joseph Leeming. Games with Playing Cards Plus Tricks and Stunts. Franklin Watts, 1949. ??NYS -- but two abridged versions have appeared.

Games and Fun with Playing Cards. Dover, NY, 1980. This contains everything except the section on bridge.

Tricks and Stunts with Playing Cards Plus Games of Solitaire. Gramercy Publishing, NY, nd [1960s?]. This includes all the tricks, stunts, puzzles and solitaire games.

25 Puzzles with Cards, 8th puzzle. Tricky triangle. Dover: pp. 154-155 & 172. Gramercy: pp. 45-46 & 65. Both have fig. 25 & 42.

Young World. c1960. P. 7: fifteen coin problem. Reverse a triangle with five on a side by moving five coins.

Robert Harbin. Party Lines. Op. cit. in 5.B.1. 1963. Birds in flight, p. 34. Says this problem is described by Gardner, but gives no specific source.

Maxey Brooke. (Fun for the Money, Scribner's, 1963); reprinted as: Coin Games and Puzzles, Dover, 1973. Prob. 4: Bottoms up, pp. 15 & 75. On p. 6, he acknowledges Leopold as his source. Thanks to Heinrich Hemme for this reference.

D. B. Eperson. Triangular (old) pennies. MG 54 (No. 387) (Feb 1970) 48 49. The number of pennies which must be moved to reverse a triangle with n on a side is [T(n)/3], where T(n) is the n th triangular number, which is the number in the array.

James Bidwell. The ten coin triangle. MTg 54 (1971) 21 22. How many coins must be moved to reverse the triangle with n on an edge? His students find the same value as Eperson, but they weren't sure they had proved it.

Putnam. Puzzle Fun. 1978. No. 25: Triangular reverse, pp. 6 & 31. Usual 10 coin triangle.