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Milo thought that

We would have to test all 25 numbers to be sure what his rule was. Do you agree?

Helen of Lea Valley Primary school had a good idea:

For the "I like these numbers" I put $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24\}$ because they are even and for "I don't like" I put $\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25\}$ because they are odd.

Kate of Bilton Junior School exclaimed:

It is the five times table, well it has to be! What do you think?

Rischabh of the European School of Varese was unsure and wants more information:

It is either odd numbers, or the five times table. I would like to try number $7$. If it goes on the left, it means it's the odd numbers, and if it goes on the right, it's the five times table. I will also try $10$ to be sure.

What if the number $7$ and the number $10$ went into the "I don't like" section. Are there any other possibilities?

Simran said: The rule might be to select the numbers with units of $5$.

On the other hand what might the rule be if we tried $7$ and $10$ and both numbers went into the "I like" section?

We would have to test all 25 numbers to be sure what his rule was. Do you agree?

Helen of Lea Valley Primary school had a good idea:

For the "I like these numbers" I put $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24\}$ because they are even and for "I don't like" I put $\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25\}$ because they are odd.

Kate of Bilton Junior School exclaimed:

It is the five times table, well it has to be! What do you think?

Rischabh of the European School of Varese was unsure and wants more information:

It is either odd numbers, or the five times table. I would like to try number $7$. If it goes on the left, it means it's the odd numbers, and if it goes on the right, it's the five times table. I will also try $10$ to be sure.

What if the number $7$ and the number $10$ went into the "I don't like" section. Are there any other possibilities?

Simran said: The rule might be to select the numbers with units of $5$.

On the other hand what might the rule be if we tried $7$ and $10$ and both numbers went into the "I like" section?