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

+1 vote
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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.

posted Jun 8, 2015

+1 vote

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

answer Jun 8, 2015

Similar Puzzles

Below shows the first 5 positive integers formed by using the four mathematical operators (+ - * /) only on the digit 4 four times.

``````1 = 44 / 44
2 = 4*4 / (4+4)
3 = (4+4+4) / 4
4 = 4 + (4*(4-4))
5 = (4+(4*4)) / 4
``````

What is the smallest positive integer that cannot be represented using these conditions?