Question

What are the largest and smallest 5-digit numbers that satisfy the following conditions?

A. Each digit of the number is a prime digit.
B. Each successive pair of digits forms a 2-digit number that is NOT a prime number.
C. Each of the prime digits must appear at least once in the 5-digit number.

Answer 1

the digits we can use are 2 , 3 ,5 and 7

since every pair of two digits in a five digit number can't be prime

so we can't have , 23 , 53 and 73 , so 3 must be at first place in any case

for the largest number we have
3 5 7 7 2

and smallest number is
3 2 2 5 7