Postman Nat delivers the mail in a small village which has only one street with exactly ten houses, numbered from 1 up to and including 10.

In a certain week, Nat 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?

((3*(10+9+8+7+6+5+4+3+2+1))
 - (18+12+23+19+32+25))/3 = 12
Therefore, the two houses are one of the four pairs:
(2,10),(3,9),(4,8),(5,7)

Four houses were delivered on each day (except Sunday),
with the total of 32 on Friday. For 32, the four houses on Friday
were (10,9,8,5) or (10,9,7,6). The fact that 10 and 9 are in both
sets means that two of the four pairs, (2,10) and (3,9), are eliminated as possibilities. With (10,9,8,5) having one element of each of the two remaining pairs requires the Friday delivery to have been (10,9,7,6). Which leaves only the pair (4,8) as the undelivered.
Thus...
the two houses that did not get any mail that week were 4 and 8.

Posted by Dej Mar on 2013-06-12 02:27:32