Four boys were playing marbles; their names were Gary, Henry, John, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Gary shot before Henry and Alice. Alice was older than the boy with 15 marbles. Henry had fewer than 15 marbles. Alice shot before Henry. John shot after Henry. If John was 10 years old, he did not have 15 marbles. Gary and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Henry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy?

Question

Four boys were playing marbles; their names were Gary, Henry, John, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Gary shot before Henry and Alice. Alice was older than the boy with 15 marbles. Henry had fewer than 15 marbles. Alice shot before Henry. John shot after Henry. If John was 10 years old, he did not have 15 marbles. Gary and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Henry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy? ​

Quizplus · Accepted Answer

From the clues given, we can deduce the following:
- One of the boys had 9 marbles, another had 15, and each of the other two had 12.
- Gary shot before Henry and Alice.
- Alice was older than the boy with 15 marbles.
- Henry had fewer than 15 marbles.
- Alice shot before Henry.
- John shot after Henry.
- If John was 10 years old, he did not have 15 marbles.
- Gary and Alice together had an even number of marbles.
- The youngest boy was not the one with 15 marbles.
- If Henry had 12 marbles, he wasn't the youngest.
- The 10-year-old shot after the 17-year-old.

From the first clue, we can determine that the boy with 9 marbles must be one of John or Henry. This eliminates Gary and Alice from being either of the boys with 9 marbles.

From the second and fifth clues, we know that Gary and Alice come before Henry, so neither of them can have 9 marbles. This means that either John or Henry has 9 marbles.

From the third clue, we know that Alice is older than the boy with 15 marbles. This eliminates John from being the boy with 15 marbles, since he is only 10 years old.

From the fourth clue, we know that Henry has fewer than 15 marbles. Since Gary and Alice each have 12 marbles, Henry must have 9 or 12 marbles. From the eleventh clue, we know that if Henry has 12 marbles, he wasn't the youngest, so he must have 9 marbles. This means that John has 12 marbles.

From the sixth clue, we know that John comes after Henry, so John must be either 17 or 18 years old. From the tenth clue, we know that the 10-year-old shot after the 17-year-old, so John must be 18 years old.

From the seventh clue, we know that the 10-year-old did not have 15 marbles, which means that John does not have 15 marbles. This means that either Gary or Alice has 15 marbles.

From the eighth clue, we know that Gary and Alice together have an even number of marbles. Since we know that one of them has 15 marbles, this must mean that the other has 9 marbles (since John and Henry each have 12 and the sum of their marbles is even).

From the ninth clue, we know that the youngest boy did not have 15 marbles, which means that Gary must be the youngest at 3 years old. This means that Alice is 18 years old.

Therefore, the ages of the boys are:
John - 18
Henry - 9
Gary - 3
Alice - 18

The answer is D.

Four Boys Were Playing Marbles; Their Names Were Gary, Henry