Rampaging Primes

Logic Level 4

$M$ is the largest $5$ -digit number and $N$ is the smallest $5$ -digit number that satisfies the following conditions ---

Each digit of the numbers is a prime digit
Each successive pairs of digits forms a $2$ -digit number that is NOT a prime number
Each of the prime digits must appear at least once in each of the $5$ -digit numbers

Find $M-N$

The answer is 3515.

1 solution

Satyen Nabar
Mar 23, 2016

$2, 3, 5, 7$ are the prime digits to satisfy criterion One.

The pairs that satisfy criterion Two are $22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77$

$33$ is the only pair that has $3$ as the second digit. So the number must start with $3$ to satisfy criterion Three.

Rest is simply choosing from the above pairs to make up $35772$ as the largest and $32257$ as the smallest numbers.

Difference is $3515$

Your question may need to be clearer, at the moment i read it as over both numbers it must include 7532, but not necessarily all included in each number

Stuart Page - 5 years, 2 months ago

Rampaging Primes

The answer is 3515.

1 solution

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