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

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Primes Make One Square

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factor Lines

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Squares

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One Wasn't Square

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Money Bags

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions in a Box

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mystery Matrix

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Moons of Vuvv

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapes on the Playground

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Numerically Equal

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Forgot the Numbers

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Egyptian Rope

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadrilaterals

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prison Cells

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Neighbours

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Puzzling Sweet Shop

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chain of Changes

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A City of Towers

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2, 4, 6, 8

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mixed-up Socks

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 6 Beads

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Dice

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Five Coins

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Triangles Puzzle

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Let's Investigate Triangles

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Cuboids

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Boxes

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plants

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

Age 5 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Numbers

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

Age 7 to 14

Challenge Level