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:
- 2 (An even prime number)
- 3 (The smallest odd prime number)
- 3 (A number whose factors add to 4)
- 13 (A number that Blur, Black Sabbath, Havoc, and many others have named albums after)
- ? (The key that was used to encode the message in part 4)
- 17 (The sum of four consecutive prime numbers)
- 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
The answers are:
- 12 (After all 12 days, how many partridges has my true love given me?)
- 28 (How many items does my true love give me on the seventh day?)
- 12 (After 12 days, how many drummers drumming has my true love given me?)
- 364 (After 12 days, how many items has my true love given me?)
- 40 (After 12 days, how many gold rings has my true love given me?)
- 9 (On which day does the total number of items that my true love has given me first exceed 150?)
- 120 (After 8 days, how many items has my true love given me?)
- 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“.
More from Chalkdust
- Did you solve it?
- We have a go at the puzzles in Daniel Griller’s new book
- Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
- Find out more about the spiral trees on the cover of Issue 09
- Did you solve it?
- This month’s round up of mathematical blog posts from all over the internet