Brain Game: 5 Coins in a Pool
I'mÂ eager to hear your thoughts onÂ today's puzzle,Â since it mixes a bit of math with a logic puzzle and some deductive reasoning.Â The puzzle may be tough, but it's clearly solvable. It just takes a close examinationÂ of the given information and the possibilities rendered. Here we go; good luck!
Five siblings - Barry, Carrie, Harry, Larry, and Mary - were learning how to swim. Once they became good enough to swim to the bottom of the pool and back up, the kids' father used to toss coins in the pool. They'd sink to the bottom, and the youngsters would dive down to retrieve them.
On one such instance, the dad looked into his pocket. He had five coins totalling 91 cents, and he threw all five of them into the pool. The kids dove in, and each rose to the surface with one of the five coins. Based on the following two clues, can you determine which child retrieved which coin?
1. Harry's coin was worth
one-fifth as much asÂ Mary's coin.
2. Carrie's coin was worth
ten times as much asÂ Barry's coin.
Here is the SOLUTION.
BarryÂ foundÂ a penny,
Carrie foundÂ a dime,
Harry foundÂ a nickel,
Larry foundÂ a half-dollar, and
Mary foundÂ a quarter.
First, off, 91 cents can only beÂ represented by five coinsÂ using a combination of penny,Â nickel, dime,Â quarter, and half-dollar; so those are our denominations.
There areÂ a few different waysÂ to solve this puzzle... here's one logic sequence:
Clue 1: Since Harry's coin was worthÂ 5 timesÂ as much as Mary's, either (A),Â (B)Â or (C)Â is true:
(A) Harry had the pennyÂ AND Mary had the nickel
(B) Harry had the nickelÂ AND Mary had the quarter
(C) Harry had the dime AND Mary had the half-dollar
Clue 2: Since Carrie's coin was worth 10x as much as Barry's, either (D) or (E) is true:
(D) Barry had the pennyÂ AND Carrie had the dime
(E) Barry had theÂ nickelÂ AND Carrie had the half-dollar
So we can assume the following:
Barry has either the penny or nickel.
Carrie has either the dime or half-dollar.
Harry has either the penny, nickel, or dime.
Mary has either the nickel, quarter, or half-dollar.
We don't have any information for Larry yet.
Reviewing the clues, we can determine that (A) is not possible, because if (A) were true, then neither (D) nor (E)Â could beÂ true, and we know that one ofÂ those IS true.
Likewise, we can determine that (E) is not possible, because if (E) were true, then neither (B) nor (C) could be true, and we know that one of those IS true.
Since (E) is not possible,Â (D) is true, meaning that Barry has the penny and Carrie the dime.
By elimination, the only coin left for Harry is the nickel,Â revealing thatÂ (B) must be true. That means that Mary has the quarter, leaving the half-dollar for Larry.