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### The Third Dimension

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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### Square Corners

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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### A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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### A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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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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### Take three numbers

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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### Play to 37

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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### Build it up

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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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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### How many Times?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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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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### Got It

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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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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### Oh! Harry!

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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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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### Roll these Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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### Wonky Watches

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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### Amy's Dominoes

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

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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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### 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?

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### Dice in a Corner

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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### Watch the clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?