Logical Interview Question:

A number is called a palindrome when it is equal to the number you get when all its digits Postman Pat delivers the mail in the small village Tenhouses. This village, as you already suspected, has only one street with exactly ten houses, numbered from 1 up to and including 10. In a certain week, Pat did not deliver any mail at two houses in the village; at the other houses he delivered mail three times each. Each working day he delivered mail at exactly four houses. The sums of the house numbers where he delivered mail were: on Monday: 18 on Tuesday: 12 on Wednesday: 23 on Thursday: 19 on Friday: 32 op Saturday: 25 on Sunday: he never works Which two houses didn't get any mail that week?

Submitted by: Administrator

If postman Pat would have 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)?=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 combination 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 2 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 combination 2+10 and 3+9 are not possible. Also 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: Monday houses 1, 3, 5 and 9
Tuesday houses 1, 2, 3 and 6
Wednesday houses 1, 5, 7 and 10
Thursday houses 2, 3, 5 and 9
Friday houses 6, 7, 9 and 10
Saturday houses 2, 6, 7 and 10
Submitted by: Administrator