### 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:

"Guess my number," said Tom, "I'll only answer yes or no."

"OK. Is it less than $1000$?" "No."
"Is it less than $2000$?" "Yes."
"Is it even?" "No."
"So it's an odd number between $1000$ and $2000$?"
"Yes, but you knew that already. It's a wasted question!"
"Is it divisible by $3$?" "No."
"Is it divisible by $5$?" "No."
"Is it divisible by $7$?" "Yes."
"If I divide it by $7$ do I get a number that is less than $100$?" "No."
"Do I get a number that is less than $200$?" "Yes."
"Ah! $100 \times 7$ = $700$ and $200 \times 7 = 1400$. So your number is less than $1400$?"
"Yes, but that's another wasted question."
"Ha! $14$ squared is $196$.
So your number is $7$ times the product of two prime numbers less than $14$?"
"Yes."
"I am sure I know your number and this question is just checking.
Is your number palendromic? Does it read the same in both directions?"
"Yes."

What was Tom's number?