Take a number e.g. 537
Multiply its digits 5 x 3 x 7 = 105
Repeat with 105’s digits. 1 x 0 x 5 = 0
Stop when you reach a single digit.
So 537 took 2 steps.
Can you find a number that takes more steps? You can test your numbers here:
Then can you find the smallest number that takes 1,2,3,4… steps? Click run when you want to see the answers.
Thanks to numberphile for this problem – their video is here.