Stuck On The 'Red Haired Child' Puzzle? Here's The Solution

Yesterday, you tore your hair (perhaps red in nature) out over this puzzle.

Today, the answer, also courtesy of i09.

A quick refresher:

A couple of logicians – and former college roommates – met up after many years apart and began discussing their children. The first asked the second for his three kids’ ages, and the second replied in the typically obscure fashion of most characters in logic puzzles. Here were his clues:

"First," says the logician, "the product of my children's ages is 36."

"Second, the sum of their ages is the same as our apartment number in college."

"Third, my oldest child has red hair."

After hearing the final clue, the first logician figured out all three ages.

But how?

Here’s how i09 solves it, clue by clue.

1) “The product of my children’s ages is 36.”

Here are the triplet factors for 36:

• 1 x 1 x 36
• 1 x 2 x 18
• 1 x 3 x 12
• 1 x 4 x 9
• 1 x 6 x 6
• 2 x 2 x 9
• 2 x 3 x 6
• 3 x 3 x 4

2) “The sum of their ages is the same as our apartment number in college.”

Here are the sums:

• 1 + 1 + 36 = 38
• 1 + 2 + 18 = 21
• 1 + 3 + 12 = 16
• 1 + 4 + 9 =14
• 1 + 6 + 6 = 13
• 2 + 2 + 9 = 13
• 2 + 3 + 6 = 11
• 3 + 3 + 4 = 10

At this point, you’ll notice that all but two of those sums are unique. If their apartment number had been any of the singular results, the first logician would have recognised it immediately and answered. Instead, he needed a further clue. From this we can assume their room number was 13.

3) “My oldest child has red hair.”

The ‘red hair’ description is pure misdirection! The real keyword is “oldest.”

• 1 + 6 + 6 = 13
• 2 + 2 + 9 = 13

As you can see, only one sum leading to 13 reveals an eldest child.

Therefore, the children are aged 2, 2 and 9.

Did you get it?