Everyone who knows me will know that I love number puzzles. Everyone who knows Jake knows that he loves his maths. A dangerous combination!
When I was probably a little older than Jake is now, I was introduced to a number puzzle that I still remember, so, when Jake asked me the other day "Give me a maths question", as he does on a regular basis, I explained this number puzzle to him.
The challenge is to use the digits 1 to 4, combined with available mathematical operations, to produce every number from 1 to 100. Jake had a pretty good go at it, and we got into the 30s or 40s fairly quickly together.
However, when we moved on to something different, I carried on mulling it over, and seeing if I could work them all out.
The rules are that you can only use the digits 1 to 4 once (but it is not necessary to use all of them) and the following operations can be used: add, subtract, multiply, divide, powers and factorials.
A factorial is calculated by multiplying a given number by all numbers less than it down to 1, and it is written by putting an exclamation mark after the number. So, for example, 4 factorial is written 4! and 4! = 4 x 3 x 2 x 1 = 24. This is very useful in the puzzle.
So, to give an example, let’s think about how we can find an answer to the puzzle for the number 15.
Well, 15 = (4+1) x 3.
There are lots of other ways we could come up with an answer for 15. For example:
15 = 4! - 3^2
15 = 4^2 - 1
15 = 3! + (4 x 2) +1
15 = (4 x 3) + 2 + 1
15 = (4! / 2) + 3 and so on.
(By the way, apologies for the lack of proper notation. As per computer speak, I am using / for division, and the ^ sign to indicate raising to a power.)
So, how am I getting on. Well, I have six numbers left to do to complete the 1 to 100 set. 57 was bugging me for a while, until I came up with:
57 = ((4 + 1)! / 2) - 3
Now, the lowest of the unsolved numbers is 76.
Any comments with a solution for it gratefully received.