Magic Triangles

Nine of the ten digits are places as below on each of 2 triangles.

			A
		I		B
	H				C
G		F		E		D

			A
		I		B
	H				C
G		F		E		D

1. The sum along each triangle side was 14
2. The missing digit in the first triangle was different from the missing digit in the second.

What were the missing digits?

Answer:

The missing digits are 6 and 7

1. Construct equations for the sums of the triangles:

(A+B+C+D)+(D+E+F+G)+(G+H+I+J)=42

2. The sum of the ten digits is 45; let j represent the missing digit

A+B+C+D+E+F+G+H+I=45-J

Subtracting, we get:A+D+G=J-3

3. So since A+D+G must be 3 or greater, and j < 9

A+D+G must be between 3 and 6; J must be between 6 and 9

There are two sets of solution:

			0
		5		3
	8				9
1		7		4		2

			0
		9		5
	4				7
1		3		8		2

And:

			0
		5		9
	8				2
1		6		4		3

			0
		9		5
	4				6
1		8		2		3