# Maths Moments

Here’s a handful of five digit problems to get to grips with.

1. Can you find a five digit number which has no zeros and no digit is repeated where:

• The first digit is a prime number
• The second digit is the fifth digit minus the first digit
• The third digit is twice the first digit
• The fourth digit is the third digit plus three
• The fifth digit is the difference between the first digit and the fourth digit
• Its digital root is a prime

2. Can you find a five digit number which is four times its reverse?

3. Can you find a five digit number whose digits add to 18 and whose product is 210 and the digits increase from left to right in the number?

4. What 5 digit number am I thinking of?

• It has 2 prime digits.
• Digit 3 is the highest number.
• Digit 2 is lowest.
• Digit 5 is between digit 2 and digit 1 and is half of digit 4.
• There are no duplicates.
• Digit 1 is 1 less than digit 3.
• Digit 1 is higher than the sum of digits 4 and 5.

5. What is the 5-digit number in which the sum of the first two digits is one less than the third, the third is double the fourth, the fourth is double the last, the third is the product of the fourth and fifth, the second is five more than the first, and the first is one-eighth the third and also one-fourth of the fourth?