# Solution to Christmas conundrum #4

… and the winners

As 2017 comes to an end, it’s time to announce the winners of the fourth and final Chalkdust Christmas Conundrum!

There were 57 entries, 56 of which were correct. The five randomly selected winners are:

• Elena Petrunina
• Andy Sloane
• Molly Barker
• Israel Cerro
• Rata Ingram

You will all soon be proud owners of signed copies of Bletchley Park Brainteasers by Sinclair McKay.

## The solution to conundrum #4

In the fourth conundrum, we asked you discover our secret message. Stop reading now if you don’t want to know the answer yet.

### Part 1: prime factors

These factors were:

1. 2 (An even prime number)
2. 3 (The smallest odd prime number)
3. 3 (A number whose factors add to 4)
4. 13 (A number that Blur, Black Sabbath, Havoc, and many others have named albums after)
5. ? (The key that was used to encode the message in part 4)
6. 17 (The sum of four consecutive prime numbers)
7. 193 (The smallest prime number that is 182 more than another prime number)

The ? must be either 13 or 17 (as the factors are in order). The product of these numbers is therefore either 9980802 or 13051818. It must be 13051818 as we were told it is a 8 digit number.

### Part 2: a Vigenère cipher

The key was Fry, giving the answer Twenty-five million, one hundred and ninety thousand, three hundred and fifteen (25190315).

### Part 3: 12 days of Christmas

1. 12 (After all 12 days, how many partridges has my true love given me?)
2. 28 (How many items does my true love give me on the seventh day?)
3. 12 (After 12 days, how many drummers drumming has my true love given me?)
4. 364 (After 12 days, how many items has my true love given me?)
5. 40 (After 12 days, how many gold rings has my true love given me?)
6. 9 (On which day does the total number of items that my true love has given me first exceed 150?)
7. 120 (After 8 days, how many items has my true love given me?)
8. 55 (How many items does my true love give me on the tenth day?)

This gives the number 18160915

### Part 4: a Caesar shift

Using 17 from the first part to decode this gives fourteen million, one hundred and thirty thousand, onehundred and nineteen (14130119)

### The final message

Concatenating the four answers gives 13051818251903151816091514130119, revealing the message “Merry Scorpion-mas“.

Matthew Scroggs is a postdoctoral researcher in the Department of Engineering at the University of Cambridge working on finite and boundary element methods. His website, mscroggs.co.uk, is full of maths.
@mscroggs    mscroggs.co.uk    + More articles by Matthew

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