Henry Ernest Dudeney/Puzzles and Curious Problems/96 - Wrong to Right/Solution

by : $96$

 * Wrong to Right

Solution
The solution given by :

2 5 9 3 8 + 2 5 9 3 8 --- 5 1 8 7 6

but there are six more solutions:

1 2 7 3 4 + 1 2 7 3 4 --- 2 5 4 6 8

1 2 8 6 7 + 1 2 8 6 7 --- 2 5 7 3 4

1 2 9 3 8 + 1 2 9 3 8 --- 2 5 8 7 6

2 5 7 3 4 + 2 5 7 3 4 --- 5 1 4 6 8

2 5 8 6 7 + 2 5 8 6 7 --- 5 1 7 3 4

3 7 8 4 6 + 3 7 8 4 6 --- 7 5 6 9 2

Proof
Immediate first deductions:


 * $T$ is even.


 * $1 \le W \le 4$