All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
Mail Delivery Muse (Posted on 2013-06-11) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution answer Comment 3 of 3 |
((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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information