6.5 Dissecting a rectangle into Pythagorean triangles 223
Project: Cross number puzzle on primitive Pythagorean triples^1
123 4 56(^789)
10 11 12 13
14 15 16 17 18 19
20 21 22
23 24 25 26
(^272829303132)
33 34 35
1 B, 3 D, 9 B 29 B, 7 A, 21 D 12 B, 11 U, 20 U
2 D, 6 D, 5 B 19 U, 15 D, 7 D 22 D, 18 B, 15 U
27 A, 2 D, 26 D 20 A, 8 D, 8 A 16 A, 31 A, 33 A
5 D, 3 A, 25 B 30 D, 14 A, 9 A 16 B, 24 D, 23 B
28 D, 35 A, 3 U 30 U, 9 U, 13 D 22 A, 32 U, 32 D
4 U, 21 A, 21 D 19 U, 17 D, 10 A 32 U, 34 A, 33 A
The answers are distinct 2- and 3-digit decimal numbers, none be-
ginning with zero. Each of the above sets of answers is a primitive
Pythagorean triple, in increasing size, so that the third member is the
hypotenuse.
A=across, B=back, D=down, U=up.
For example, 1 Bhas its tens and units digits in the squares labelled 2
and 1 respectively; 11 Uis a 3-digit number with its tens and units digits
in squares 16 and 11 respectively.
(^1) R. K. Guy, Problem 1153,Crux Math., 12 (1986) 139.