### Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric.

### Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

# Tom's Number

##### Stage: 2 Challenge Level:

We knew a great deal about Tom's number, and people made good use of the information to figure out what the number was exactly.

Kevin from Etobicoke, Ontario, Canada narrowed down the answer by following the clues step by step. Once he was sure he had Tom's number, he returned to the clues to prove that his answer was the correct one. Thomas from Tattingstone Primary, near Ipswich, thought of possible answers and then arrived at his final answer by eliminating the numbers that would not work for the clues given. Holly and Joanne, from Moorfield Juniors, used a technique called guess and check; they chose a number that they estimated was reasonable and then checked it against each of the clues.

Good detective work led many of you to finding out what Tom's Number was. Ben, Malcolm and Paul from Yarm Primary School, Jake and Ben of Moorgate Primary in Tamworth, Staffordshire, Zoe of Eastbury Farm School, and classmates Matt, Adam, Dave and Chris all found the answer.

The solutions sounded very much like entries from Sherlock Holmes. Anis wrote:

From the information that was stated I can conclude that the number is:

1. Odd
2. Divisible by 7
3. Between 1000 and 1400
4. 7 times the product of two prime numbers less than 14
5. Palendromic
Joshua from Higher Bebington Junior School on the Wirral was the first in Mr Holten's class to find a solution to 'Tom's Number'. He found one particular clue to be very important. It was Anis' conclusion number 5.

Once I knew the number was palindromic I tried dividing 1331, 1221, 1111 and 1001 by 7. 1001 was the only one that gave a whole number of 143. I divided that by all the odd numbers between 7 and 11. 11 gave me the answer of 13, and as both are prime numbers, I knew that 1001 was correct.

Molly from Oaklands Primary School, Biggin Hill agrees with the solution.  She sent this pdf of her reasoning.  Well done Molly!