These activities focus on finding all solutions. Working in a systematic way will ensure no possibilities are left out.

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### School fair necklaces

How many possible symmetrical necklaces can you find? How do you know you've found them all?

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### Beads and bags

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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### Half Time

What could the half time scores have been in these Olympic hockey matches?

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### Buying a Balloon

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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### Cubes Here and There

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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### Trebling

Can you replace the letters with numbers? Is there only one solution in each case?

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### Factor Lines

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

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### Sealed Solution

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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### Magic Vs

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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### Greater Than or Less Than?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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### All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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### Finding Fifteen

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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### Button-Up Some More

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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### This Pied Piper of Hamelin

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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### Reach 100

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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### 5 on the clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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### Nine-Pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

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### Inky Cube

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?