Month: February 2020

Try to make all the numbers from 1 to 10 using exactly four fours and any number of the operators + – x / 

e.g. you can make 7 by doing 4 + 4 + 4/4

Can you make the rest?

If you are also allowed to use square root, factorial (!) and double factorial (!!) you can make the numbers 11 – 100.

e.g. 4! is 4x3x2x1 so you could make 28 by doing 4! + 4 + 4 – 4

Double factorial multiplies even or odd numbers like this:

4!! = 4 x 2

8!! = 8 x 6 x 4 x2

7!!= 7 x 5 x 3 x 1

Here is a full list of solutions if you get stuck, and watch the amazing video by Alex Bellos showing a solution for any number if you are allowed to use logarithms.

Palindromes are words or numbers that read the same back to front. e.g. ABBA, racecar, 676, 128821, and a recent date 02/02/2020.

Puzzle

Take a positive integer. Reverse the digits to get a new number. Add the two numbers together.

Repeat this process until you get a palindrome.

Some numbers end up in a palindrome quite quickly e.g. 57. 57+75=132, 132+231=363.

Some numbers take a long time – 89 takes an unusually large 24 steps (the most of any number under 10,000 that is known to resolve into a palindrome according to Wikipedia) to reach the palindrome 8,813,200,023,188.

Can you find a starting number that doesn’t end up at a palindrome? Nobody know if this is possible.

You could use this applet that we wrote in maths club to look for one

It is interesting to look for Lychrel numbers in other bases – what happens in binary?