Mathematical genius Adam Spencer, author of new book The Number Games, brings us a daily riddle designed to get your grey matter firing in the lead up to the festive season.
This puzzle is taken from the 2016 International Singapore Mathematics Competition. The ISMC is an initiative to get primary-aged schoolkids into maths and problem-solving.
"To be honest, a lot of these questions aimed at 10-year-olds will get adults thinking pretty hard!" Spencer says.
Try your luck with one of the puzzles below.
There are 4 keys and 4 locks. What is the maximum total number of unlocking attempts you need to try so as to be guaranteed to have matched all 4 keys to their locks?
Do you need a hint? Read on...
The question is asking what is the 'maximum' number of attempts you need before you have matched all keys with their locks.
Two things; firstly, try and act out the scenario where you are as unlucky as possible in randomly matching keys to locks. But secondly, notice that if you've tried all the keys but one on a lock and they've all failed, you don't have to try the last key because you know it must be the one.
Think about the unluckiest you can be in trying keys and locks. Pick up the first lock. The worst case scenario is that the first 3 keys you try all fail on the lock. If you unsuccessfully try 3 keys on the first lock, you will know that the fourth key is a match. So you don't need to try that fourth key, you only need a maximum of 3 attempts. Once you've matched that key to its lock, you have 3 locks and 3 keys left. So, the second lock needs a maximum of 2 tries, and the third only needs one. Once you've matched the first 3 locks to their keys, the remaining key obviously goes in the last lock. So there are, at most 3 + 2 + 1 = 6 tries needed to match all 4 locks to their key.
Adam Spencer's book The Number Games is available now from all good bookstores or visit adamspencer.com.au. Note: Shipping to New Zealand unavailable.