favourite number puzzle

[anotherdad]

I was doing some puzzles with my nephew at the weekend and remembered my favourite one set by an inspiring maths teacher for me many years ago. It has a lovely combination of elementary arithmetic, some logical deduction and a nice twist. Here it is for anyone (or their children) that would like to have a go at it. With the advent of the internet, the solution is easily found so if you want to enjoy the satisfaction of figuring it out, don't be tempted to cheat!

A pollster is going door-to-door to find people to complete his survey. At one house, the door is answered by a woman who, when asked how old her children are, sets the pollster a challenge.

“I’ll complete your survey if you can correctly deduce the ages of my three children from a series of clues. You have one chance to get them right, so no guessing.”

The pollster agrees and asks for an opening clue.

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

The pollster thinks for a few moments and asks for another clue.

“The sum of my children’s ages matches the number of the house down the road with the green door.”

The pollster strolls the short distance to the indicated house, sees the house number and returns to ask: “Can I have another clue, please?”

“My eldest child plays the cello.”

How old are the children?


edited to remove the horizontal line that was playing havoc with the formatting

[solimum]

Clever! Probably not a full-size cello though....

[KS10]

I cheated. I used Google to give me some clues.

[Ellarootoo]

Argh! I got it down to two options, and DD got it down to one, but I argued that both of mine were valid answers - I could see how DD’s was a better answer, but couldn’t convince myself that the other option was wrong. (Trying not to give anything away, but I’m sure those that know the right answer can guess my argument.)

I kind of knew DD’s had to be the right answer because of the framework of the question, but eventually gave in and googled to see if we’d missed something obvious. Of course, the better answer was the right answer and my argument was just me being pedantic, but I still feel silly for being sure there must be another clue I was missing.

[KS10]

Well, I got it down to two and then used solimum's post to arrive at my final answer. Still not !00% sure though.

[anotherdad]

Argh! I got it down to two options, and DD got it down to one, but I argued that both of mine were valid answers - I could see how DD’s was a better answer, but couldn’t convince myself that the other option was wrong. (Trying not to give anything away, but I’m sure those that know the right answer can guess my argument.)

I kind of knew DD’s had to be the right answer because of the framework of the question, but eventually gave in and googled to see if we’d missed something obvious. Of course, the better answer was the right answer and my argument was just me being pedantic, but I still feel silly for being sure there must be another clue I was missing.

Yes, it's that nice twist that means there is only one "correct" answer, i.e. the answer that is the ages of the children in the story, and yes, one can be pedantic with the "eldest" descriptor but the right answer is more elegant.

For those interested, you can achieve the other solution if the last clue is something like:

"My youngest child has green eyes."

[anotherdad]

Clever! Probably not a full-size cello though....

[anotherdad]

I cheated. I used Google to give me some clues.

You get marks for honesty!

[Tinkers]

With local elections coming up I might have to try this if certain individuals decide to darken my door. They might prefer this to what I did have lined up to ask them...