Main content

Today Puzzle #624

Puzzle No. 624– Tuesday 3 December

The Edinburgh Seven were matriculated at the University of Edinburgh in 1869 and were the first group of female students to do so at a British university, but they were ultimately prevented from graduating as doctors. Their campaign resulted in the 1877 legislation to ensure that women could study at university. My friend and I decide to invent a ‘7’ themed game in their honour, where the aim is to obtain a total score of ‘7’ across the rolls of three dice. If my reliable friend rolls the three dice under her hand, and tells me that at least one is a ‘4’, how likely is it that the total score obtained on all three dice is a ‘7’?

Today’s #PuzzleForToday has been set by Mary Llwellyn, a maths PHD student from Edinburgh University

Click here for the answer

To roll no ‘4’s there are 5 choices for each die, so there are 5 cubed = 125 possibilities from the 216 ways of rolling three dice. Therefore there are 216 - 125 = 91 ways of rolling at least one 4. Of those, 6 are ‘4’, ‘2’, ‘1’ in some order, giving a probability of 6/91.

More fiendish brain-teasers and quizzes on BBC Radio...