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

Home > Just Math
Pocket Change (Posted on 2013-07-30) Difficulty: 4 of 5
A friend of mine, Sol announces that he has a number of coins in his pocket that add up to precisely one dollar. When he tells me how many coins he has, I ask if any one of them is a half-dollar. Sol tells me "no". I realize that I can't tell for sure what coins he has, because there are six different combinations that produce precisely one dollar.

How many coins does Sol have in his pocket?

See The Solution Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 5 |
Each of the six possibilities of Sol's coins can be transformed to the others through one or more of the following relationships:
1 quarter + 3 nickels = 4 dimes
4 dimes + 5 pennies = 9 nickels
1 quarter + 5 pennies = 6 nickels
3 quarters + 5 pennies = 8 dimes
Each relation preserves the total value and total quantity of coins.

From here, I just played with possible starting configurations until I got a solution with 16 coins:
2 quarters, 4 dimes, 10 pennies
2 quarters, 9 nickels, 5 pennies
1 quarter, 4 dimes, 6 nickels, 5 pennies
1 quarter, 15 nickels
8 dimes, 3 nickels, 5 pennies
4 dimes, 12 nickels

  Posted by Brian Smith on 2013-07-30 14:43:39
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 (9)
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