Solution to: Postman Pat

If postman Pat had delivered mail three times at each house, then the total sum of the house numbers per day would be (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) × 3 = 165. Now that sum is 18 + 12 + 23 + 19 + 32 + 25 = 129. The difference is 165 - 129 = 36; divided by 3 this is 12. The sum of the house numbers where no mail was delivered is therefore 12. The following combinations are possible:

2 + 10
3 + 9
4 + 8
5 + 7

Each day, at four houses the mail was delivered. On Tuesday, the sum was 12. 12 can only be made from four house numbers in two ways:

1 + 2 + 3 + 6
1 + 2 + 4 + 5

The same holds for Friday with the sum of 32:

5 + 8 + 9 + 10
6 + 7 + 9 + 10

From this, we can conclude that the house numbers 1, 2, 9 and 10 for sure have received mail, which means that the combinations 2 + 10 and 3 + 9 are not possible. In addition, the combination 5 + 7 is not possible, because mail was delivered either at house 5 or at house 7. Thus the only remaining solution is: houses 4 and 8.

N.B.: there are various possibilities for the actual post-delivery of the whole week. For example:

Copyright © 2002 E.R. van Veldhoven. All rights reserved.

Back to the puzzle