Can you solve our Christmas puzzle?

Olivia Miller

In the spirit of Christmas, Professor Peter Hydon and Dr Daniel Bearup from the School of Mathematics, Statistics and Actuarial Science, have developed a brain-teasing puzzle for the festive period.

Titled ‘Scrooge’s Christmas charity’, the puzzle sees Ebenezer Scrooge having a change of heart from his usual ‘Bah humbug’ self and becoming a generous benefactor. Yet, he needs some help with organising his finances. See the full puzzle below…

Scrooge’s Christmas charity

After the events narrated by Charles Dickens in A Christmas Carol, the miserly and miserable Ebenezer Scrooge became a generous benefactor to many and was loved by all. He even enabled his former clerk Bob Cratchit to set up his own little business as an accountant, so that his family need never starve again. “Honest Bob” was known for carrying out his work faithfully and accurately, keeping strictly to the terms on which he was employed.

One Christmas, Scrooge gave Bob a small problem and a sack containing 500 gold sovereigns.

‘It’s a disgrace that the nine orphanages in our part of London don’t have enough income to feed their little ones. Remember Tiny Tim! This money is my entire profit for the year. I want to use it to help as many of these orphanages as possible, but they must all receive the same number of sovereigns. I don’t want any of those I help to find out that they were given less than the others.

‘The trouble is that nine doesn’t divide five hundred exactly, nor does eight, seven or six. So, I think that I can only give to five orphanages, but I’d like to do more. Can you help me?’

Bob thought for a few seconds (being fast at arithmetic), then replied.

‘Yes sir, I can help you. My usual management fee applies, of course. If I try to split the remainder between nine orphanages, there are four sovereigns too few. I cannot give an equal share to eight orphanages, either, because there would be one sovereign left over. However, seven orphanages will benefit, if you wish me to handle this.’

Scrooge was delighted and agreed at once.

‘Bless you, Bob; you have made this a truly happy Christmas for the orphans.’

Question: What was Bob’s management fee?

Bonus question: What is the moral of this puzzle?

View Scrooge’s Christmas puzzle solution for the answers.