BrainTwister #37: Digital multiplication

#37 Digital multiplication

Set by Mary Ellis

Consider the following rule: Start with any two-digit number, then repeatedly multiply the digits together until the result is a one-digit number. For example: 84 ⇨ 32 ⇨ 6, or 97 ⇨ 63 ⇨ 18 ⇨ 8.

What happens if you start with 93?

There is just one sequence of length 5 starting from a two-digit number. This sequence ends with the number 8. What must the starting number be?

Can you find the longest possible sequence starting from a three-digit number?

Solution next week

#36 Prime generators

Solution

Setting p = 5 generates four primes (5, 7,…