Madadian Mail
Published in Brain Teasers
If postman Patel 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)x3=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
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. 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.
Today's brain teaser courtesy of Braingle.com.