Interview Question 3780

Created by admin on Mon, 19/11/2012 - 12:57
Question: 

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?

Language: 
Puzzles
Answer: 

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)×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 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

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.