MathDB

Each two-digit natural number is assigned a digit as follows: Its digits are multiplied. If the result is a digit, this is the assigned digit. If the result is a two-digit number, these two figures are multiplied, and if the result is a digit, this is the assigned digit. Otherwise, the operation is repeated. For example, the digit assigned to

32

6

since

3 \times = 6

; the digit assigned to

93

4

since

9 \times 3 = 27

2 \times 7 = 14

1 \times 4 = 4

. Find all the two-digit numbers that are assigned

8

Problem Statement