### An Interesting Maths Problem

#### By seanharris on Jul 04, 2007

I encountered the following problem a number of months ago and spent a couple of days mulling over it before I managed to get the answer. I thought I would post it here so other could enjoy stretching some of the lesser used parts of the brain, Have fun.

Three gentlemen go to a restaurant for Lunch. At the end of the meal the waiter tells them that the bill is £30 so they each give him £10. The waiter takes this to the cashier who says "No, no, no, you have got it wrong the bill was only £25 here is £5 to take back to the gentlemen". On the walk back to the table the waiter thinks a) £5 does no divide well by 3, b) The gentlemen do not know that they have been over charged and were happy to pay the bill that they were given and c) they may or may not leave a tip but I can't be sure. So he pockets £2 and gives each of the men £1 each explaining that there was a mistake in the bill (but not telling them them by how much).

Q1) Now each gentleman paid £10 to start and got £1 back so how much did they spend on lunch?

A) £9

Q2) So how much did they spend in total?

A) £27

Q3) Plus the £2 in the waiters pocket makes a total of?

A) £29

So where is the additional £1?

The £27 (total spent) already includes the £2 taken by the waiter. The misdirection occurs when an additional £2 is added to the £27 figure. There is no missing £1: They each spent £9 for a total of £27-- £25 went to the restaurant and £2 went to the waiter.

Posted by

Josh Simonson July 04, 2007 at 05:16 AM BST #