The solution to yesterday's teaser

Skip back to yesterday if you missed it.

How old are Jane's kids? OK...
Jane tells John "the product of their ages is 36"

How many different ways can you multiply three whole numbers together to get 36? Let's try:

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

Jane says to John that "the sum of their ages is the same as your house number."

We don't know where John lives but let's add up the possibilities anyway:

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

I hope John would know his own house number, but he says he still can't work out the kids' ages. How can this be?

Well, if John lived at number 36, 21, 16, 14, 11 or 10 he would have worked it out by now. There's only one sum for each where the ages multiply up to 36. ie if John lived at No. 14 he would know Jane's children were aged 1, 4 and 9.

So John must live at number 13.

We now have two possibilities: 1, 6 and 6 or 2, 2, and 9.

Jane tells him that "The oldest one has red hair." So the children can't be aged 1, 6 and 6 or there would be two oldest.

So Jane's children are aged 2, 2, and 9.

Hope I didn't cause too many headaches :)

The problem for next week is to come up with a solution to the world's financial crisis so I can take early retirement this year with no loss of income. Should be easy after this warm up.