1. The Missing Number Can you help PC Slade?

2. PC Slade has been given the task of identifying a missing number that will unlock the mystery location of the robbers following a bank robbery. He knows several things about the number from his investigation, but so far he is unable to piece them together. He knows for definite that the number he is looking for is less than 100, but it’s not a multiple of 5, and it’s certainly not a prime. He was told by another reliable investigator that if you reverse the digits of the number you do get a prime number!... The number only has only four factors, and Mr Slade has worked out that the sum of its digits is also a prime! As you can see he’s done a lot of work on this investigation already but he’s stuck! Another colleague of Mr Slade has also been working on the case and has found out some extra information. She found out that it’s not a square number and it’s also one more than a multiple of three. One of the witnesses to the crime overheard the bank robbers talking about this secret number as they tried to escape. The witness heard them say that one of its digits is a prime number, and if you multiply the number by 5 your answer is greater than 100!

3. Clues… It’s less than 100 It’s not a multiple of 5 It’s not prime If you reverse its digits you get a prime number It has four factors The sum of its digits is prime It’s not a square number It’s one more than a multiple of three One of its digits is a prime number If you multiply it by 5 your answer is greater than 100

4. Which maths topics will I need to use? What do I already know about these topics? What do I need to find out? IDENTIFY

6. The robbers postcode Now that you have identified the mystery number, you have cracked a key part of the investigation to find the bank robbers! The number you have found forms part of their postcode. CF34...... The rest of the postcode is still missing and PC Slade needs your help once again to solve the problem.

7. Finding the rest of the postcode Mr Tan, a rogue police informer, has told you that the next number part of the postcode is hidden within the prime factors of the number 360. The next number is the largest prime factor of 360. The informer can teach you about prime factors at his help station. The last two letters of the postcode are the corresponding letters of the alphabet to the two other prime factors of 360. e.g. A = 1, B = 2 etc

8. Help Station 150 2 75 3 25 5 5 150 = 2 x 3 x 5 x 5 150 = 2 x 75 75 = 3 x 25 25 = 5 x 5 Question: Write 150 as a product of it’s prime factors.