Each digit must appear exactly once. The '29' can only be formed by four different digits if those digits are 5, 7, 8, and 9. Two of those digits are shared with the '15' and they must be the smallest digits (5 and 7). The remaining two digits of the '15' are 1 and 2. The remaining three squares must be 3, 4 and 6.

The '19' requires using the highest four numbers available (the 2, the 7, the 4, and the 6). We now know some of the number in the final answer.

The '22' can be completed only by choosing 4 and 8. Now all the numbers are known.