# Thursday

CHALLENGE

These challenges are tricky - you don't have to do them!

If you have a go - Well Done!

If you need a clue scroll down the page.

The questions below  test your knowledge of multiples and involve remainders.

1. I'm thinking of a number that is 1 more than a multiple of 7.
My friend is thinking of a number that is 1 more than a multiple of 4.
Could we be thinking of the same number?

2. I'm thinking of a number that is 3 more than a multiple of 5.
My friend is thinking of a number that is 8 more than a multiple of 10.
Could we be thinking of the same number?

3. I'm thinking of a number that is 3 more than a multiple of 6.
My friend is thinking of a number that is 2 more than a multiple of 4.
Could we be thinking of the same number?

How to solve them

PURPLE PROBLEMS

1.  Using lowest common multiples again : multiply 7 by 4 to get 28  add 1 is 29.

Both people could think of 29.

So the friend thinks of 28 + 1 as one more than a multiple of 4,

and the other person thinks of  28 + 1 as one more than a multiple of 7.

both have thought of the same answer.

2. Write down multiples of 5 and add 3 to them

Write down the multiples of 10 and add 8 to them.

Some of the numbers will be the same because 8 more than a multiple of 10 is the same as 3 more than a multiple of 5 which ends in 5.

3. Write down multiples of 6 and add 3 to them

Write down the multiples of 4 and add 2 to them.

You should notice that none of the numbers are the same.

No, you can not have been thinking of the same number because 3 more than a multiple of 6 is always  an odd number and 2 more than a multiple of 4 is always an  even. number

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