dreadedmonkeygod . net

I love brain teasers. But it really burns me when the question turns out to have a problem.

In this case, I'm talking about the 1960 Popular Science Puzzle posted to BoingBoing yesterday. In an update to the solution, a reader starts his comment with, "Here's why I think the answer to the 1960's puzzle is bullshit:"

And I agree. Here's the puzzle (dmg copy):

The census taker, placing one weary foot after another, climbed the steps and rang the bell. "How many people live here?" he asked the person who answered the door.

"Three," was the prompt answer.

"And their ages?"

The reply startled him: "The product of our ages is 225, while the sum is the same as the house number."

The census taker looked up to check the number he had already noted on his tally sheet. "Hmm," he said, "I need to know one more thing: Are you the eldest?"

"Why, yes," the person said. And the census taker, cheered at the novel answers, smiled as he wrote down their ages and walked away.

Now, here are the clues gleaned from the above:

• There are three ages: a, b, and c
• a + b + c = house#
• a * b * c = 225
• The census taker knows the house number.
• The census taker didn't know whether the speaker was the oldest.

Now, I quickly factored 255 as: 1 * 3 * 3 * 5 * 5 = 255. And there are only so many ways to multiply those factors together into three ages. My hand-scribbled list has slashes through it, so I pasted this one from BoingBoing:

• 9 + 5 + 5 = 19
• 15 + 15 + 1 = 31
• 15 + 5 + 3 = 23
• 25 + 9 + 1 = 35
• 25 + 3 + 3 = 31
• 45 + 5 + 1 = 51
• 75 + 3 + 1 = 79
• 225 + 1 + 1 = 227

Now, the census taker knows the house number, and still needs more information to narrow the possibilities. There's only one sum ("house number") that leaves any ambiguity, and that's 31. So we're left with two possible age combinations:

• 15 + 15 + 1 = 31
• 25 + 3 + 3 = 31

Now, we know that the census taker didn't know whether he was talking to the oldest. So my thinking is: If the census taker is talking to a 1- or 3- year-old, he knows he's not talking to the oldest. If he's talking to a 25-year-old, he knows he is talking to the oldest. So he must be talking to a 15-year-old.

So the people in the house must be 15, 15, and 1.

Nope. The thinking of the people who wrote the puzzle is this: There exists an "oldest", therefore he can't be talking to a 15-year-old twin. And if he were talking to a 1- or 3-year-old, he'd know he was not talking to the eldest. So he must be talking to a 25-year old.

So, basically, the authors of the puzzle accept the premise that the census taker might be a moron who can't tell a 25-year-old from a 15-year-old from an infant or toddler.

So yeah. The question is flawed.

This is a big part of why I like tavern puzzles so much: there's no way that anyone can hand you the puzzle wrong.