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.
Let’s say we assign each letter of the alphabet a different number.
The value of a word is the value of the sum of its letters.
For example:
A = 1
B = 2
C = 3, etc.
What is the value of the word FOUR? Answer = 6 + 15 + 21 + 18 = 60
A number is “nice” if its value is equal to itself.
Now, you can use any assignment of letters to integers you like (provided each letter is assigned to a distinct integer).
Can you find an assignment of letters for which all of the values from 1 to n are “nice”?
What is the largest value of n? Answer here.
We found this solution for the assignment of the letters.