**Maths Challenge 1 (November 11th)**

There are 100 lockers in the long front hall of our school. Each August, the custodians add a fresh coat of paint to the lockers and replace any of the broken number plates. The lockers are numbered from 1 to 100.

When the students arrive on the first day, they decide to celebrate the start of the school year with our school tradition. The

At the

When the students arrive on the first day, they decide to celebrate the start of the school year with our school tradition. The

**first**student inside runs down the hall opening all of the lockers. The**second**student runs down the hall closing every second locker, beginning with locker number 2. The**third**student reverses the position of ever third locker, beginning with locker number 3. (If the locker is open, she closes it. If it’s closed, she opens it.) The**fourth**student changes the position of every fourth locker, beginning with number 4. This continues until the 100th student has a turn, changing the position of the 100th locker.At the

**end**of this ritual, which locker doors are open?**Maths Challenge 2 (November 18th)**

**Maths Challenge 3 (November 25th)**

How many Squares on a Chessboard?

**Maths Challenge 4 (January 10th)**

**In a 6 x 4 milk crate arrange 18 bottles so that when added vertically or horizontally the number of bottles when added is always even.**

**Maths Challenge 5 (January 27th)**

(i) A little monkey had 60 peaches.

On the first day he decided to keep 3/4 of his peaches.

He gave the rest away. Then he ate one.

On the second day he decided to keep 7/11 of his peaches.

He gave the rest away. Then he ate one.

On the third day he decided to keep 5/9 of his peaches.

He gave the rest away. Then he ate one.

On the fourth day he decided to keep 2/7 of his peaches.

He gave the rest away. Then he ate one.

On the fifth day he decided to keep 2/3 of his peaches.

He gave the rest away. Then he ate one.

How many did he have left at the end?

**Maths Challenge 6 (February 10th)...**you may present your solution with diagrams, photographs etc

**Domino Sets**

When you buy a set of 0-6 dominoes they often come in cardboard boxes - and those boxes sometimes don't last very long!

What if you were given lots of dominoes in a bag?

Before you started playing it might be a good idea to find out if you have a full set!

How would you go about it?

How could you be sure?

What if someone gave you some 0-9 dominoes?

How many do you think there would be in a full set?

What if you were given lots of dominoes in a bag?

Before you started playing it might be a good idea to find out if you have a full set!

How would you go about it?

How could you be sure?

What if someone gave you some 0-9 dominoes?

How many do you think there would be in a full set?

**Maths Challenge 7 (February 17th)**

**Nim-7**

This is a basic form of the ancient game of Nim.You will need seven objects, such as counters or blocks. It is a game for two players.

Place the 7 counters in a pile and decide who will go first. (In the next game, the other player will have the first turn.)

Each player takes turns to take away either one or two counters.

The player who takes the last counter wins.

Keep playing until you work out a winning strategy.

Does it matter who has the first turn?

What happens when you start the game with more counters?

**Maths Challenge 8 (February 24th)**

**Can you discover this special number:**

My number is special because by adding the sum, of its digits to the product of its digits gives me the original number.

What could my number be?

(Hint: try 24. The sum of its digits is 6.

The product of its digits is 8.

Since 6 add 8 is not 24 then 24 is NOT the special number)

**Maths Challenge 9 (March 3rd)**

1, 2, 3, 4, 5, 6

Can you order the digits 1,2,3,4,5 and 6 to make a number which is divisible by 6 ...

... so that when the final or last digit is removed it becomes a 5-figure number divisible by 5?

And when the final digit is removed again it becomes a 4-figure number divisible by 4?

And when the final digit is removed again it becomes a 3-figure number divisible by 3?

And when the final digit is removed again it becomes a 2-figure number divisible by 2, then finally a 1-figure number divisible by 1?

Can you order the digits 1,2,3,4,5 and 6 to make a number which is divisible by 6 ...

... so that when the final or last digit is removed it becomes a 5-figure number divisible by 5?

And when the final digit is removed again it becomes a 4-figure number divisible by 4?

And when the final digit is removed again it becomes a 3-figure number divisible by 3?

And when the final digit is removed again it becomes a 2-figure number divisible by 2, then finally a 1-figure number divisible by 1?

**Maths Challenge 10 (April 4th)**

**Negative Numbers**

I have some strange dice: the faces show the numbers 1 to 6 as usual, except that the odd numbers are negative (i.e. -1, -3, -5 in place of 1, 3, 5). If I throw two such dice, which of the following totals cannot be achieved?

A) 3

B) 7

C) 8

**Maths Challenge 11 (April 11th)**

What do you need to find a chosen number from this hundred square?

Four of the clues below are true but do nothing to help in finding the number.

Four of the clues are necessary for finding it.

Here are eight clues to use:

- The number is greater than 9.
- The number is not a multiple of 10.
- The number is a multiple of 7.
- The number is odd.
- The number is not a multiple of 11.
- The number is less than 200.
- Its ones digit is larger than its tens digit.
- Its tens digit is odd.

Can you sort out the four clues that help and the four clues that do not help in finding it?

Addition & subtraction. Divisibility.Mathematical reasoning & proof.Odd and even nu

**Maths Challenge 12 (April 25th)**

**Maths Challenge 12 (May 12th)**