John's dad picks him up from school every third day. Aaron's mum picks him up from school every other day. If they meet on the first day, how many times will they meet over three weeks?


John's dad picks him up on day: 1 4 7 10 13 16 19
Aaron's mum picks him up on day: 1 3 5 7 9 11 13 15 17 19.

So the days they meet are: day 1, 7, 13 and 19.

However, the answer supposed to be 3 not 4. Does anyone know why?
They did not mention that the first day does not count.

My dd came up with an explanation that since they go to school 5 out of 7 days so in three weeks that would be 3x5=15 days. And in the 15 days there are then only 3 times they meet.
However, we don't know which days the weekend falls on so not tusre what is the right way to approach it.

Any maths experts please enlighten us with your wisdom.

I don't think they are counting the first day as it says 'over the next three weeks'.

Not a very well posed question IMO.

Are we to assume a standard school week of Monday - Friday?

If so what do the phrases 'every third day' and 'every other day' mean in this context.

e.g. If John's dad picks him up on a Monday he will next pick him up on a Thursday. That much is clear, but when will he next pick him up? 3 days on from Thursday is Sunday, a non-school day. So will he next pick him up on the Monday or does it mean every 3rd school day which would mean he would pick him up on the Tuesday?

If you discount weekend days, the pattern is:

John: Mon1, Thu1, Tue2, Fri2, Wed3
Aaron: Mon1, Wed1, Fri1, Tue2, Thu2, Mon3, Wed3, Fri3

So they meet on the first Monday, the second Tuesday and the third Wednesday.

But yes it's a badly worded question.