There are **322** NRICH Mathematical resources connected to **Working systematically**, you may find related items under Thinking Mathematically.

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Can you fill in the empty boxes in the grid with the right shape and colour?

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

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

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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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Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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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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Can you make square numbers by adding two prime numbers together?

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

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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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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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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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Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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Can you draw a square in which the perimeter is numerically equal to the area?

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On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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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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The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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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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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?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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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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In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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Find all the numbers that can be made by adding the dots on two dice.

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Ben has five coins in his pocket. How much money might he have?

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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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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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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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