Please see if you understand the question we found in a game called Cranium!?

Question

What is the most money you could have in coins (excluding one- and two-dollar coins) and still not be able to give exact change for $1?

the answer is $1.19

the explanation for it is Three quarters, four dimes, and four pennies.

thanks

Answer 1

you could've figured that out yourself. it's called deductive reasoning, homeslice.

Answer 2

What is there not to understand?

.75 + .40 + .04 = $1.19

If you had that exact amount, you couldn't give someone a dollar in change because:

.75 + .30 = $1.05

.75  + .20 + .04 = .99

It's not possible to get exactly one dollar from that combination of coins.

Answer 3

The reason for this is you want to get the highest number of each coin possible.

If you use a fourth quarter, you're going to equal exact change for a dollar. This restricts you to 3 quarters

If you use five dimes, you're going to be able to use all five of those, plus two of those quarters to make a dollar. This restricts you to 4 dimes.

If you use five pennies, you'll be able to use all five of those penies, two of those dimes, and all three of those quarters to make a dollar. This restricts you to 4 pennies.

So, you have to make sure none of those add up by progressively using the largest amount of each coin without them adding up to an exact dollar with any combination.

Answer 4

Isn't that amazing!

Answer 5

If someone asked you for change for a dollar and you had 3 quarters, 4 dimes, and 4 pennies, you couldn't give it.  There's no combination that makes $1.00.

However, if you have 4 quarters, 1 dime, and 9 pennies, you could.  Same amount, different configuration.

If you had $1.20, there is no possible combination you could have where you could not also have a combination totaling exactly $1.00