Solution: Coin-cerned About Change
The logic for the original problem is as follows:
When you look at the contents of one canister, you can follow a process
of elimination to identify the contents of the other two canisters. This
is possible because each canister is mislabeled, which means that only
two of the three possible coin combinations can be inside a given canister.
For example, two dimes could be in either the canister labeled 15
cents , or the canister labeled 10 cents. Likewise two
nickels could be in the 15 cents or 20 cents containers,
and a dime and a nickel could be in either the 10 cents or 20
cents containers. The table below shows the different canisters
and their possible contents.
| Canister |
Possible Contents
|
| 10 cents |
one nickel , one dime |
two nickels |
| 15 cents |
two nickels |
two dimes |
| 20 cents |
two nickels |
one nickel, one dime |
When you open a canister and look at its contents, you eliminate the
combination you discover from the other canister where it could have
occurred. For example, if you discover two dimes in the 15 cents canister,
you know that that combination cannot occur in the 10 cents canister.
| Canister |
Possible Contents
|
| 10 cents |
one nickel , one dime |
two nickels |
| 15 cents |
two nickels |
two dimes |
| 20 cents |
two nickels |
one nickel, one dime |
From there it only follows that since one nickel and one dime is the
only possible combination for the 10 cents canister, it cannot
be in the 20 cents canister.
| Canister |
Possible Contents
|
| 10 cents |
one nickel , one dime |
two nickels |
| 15 cents |
two nickels |
two dimes |
| 20 cents |
two nickels |
one nickel, one dime |
This process of elimination leads you to the conclusion that the 10
cents canister contains one nickel and one dime, the 15 cents container
contains two dimes, and the 20 cents canister contains two
nickels. Regardless of which canister you start with or what combination
you see, this same process will work.
| Canister |
Possible Contents
|
| 10 cents |
one nickel , one dime |
two nickels |
| 15 cents |
two nickels |
two dimes |
| 20 cents |
two nickels |
one nickel, one dime |
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