Resources tagged with: Trial and improvement

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Broad Topics > Thinking Mathematically > Trial and improvement

Prison Cells

Age 7 to 11 Challenge Level:

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?

Difference

Age 7 to 11 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Paw Prints

Age 7 to 11 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

A Shapely Network

Age 7 to 11 Challenge Level:

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Twenty Divided Into Six

Age 7 to 11 Challenge Level:

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?

Number Round Up

Age 5 to 7 Challenge Level:

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Find the Difference

Age 5 to 7 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Sticky Dice

Age 7 to 11 Challenge Level:

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Eggs in Baskets

Age 5 to 7 Challenge Level:

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Arranging the Tables

Age 7 to 11 Challenge Level:

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Four Colours

Age 5 to 11 Challenge Level:

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Number Juggle

Age 7 to 11 Challenge Level:

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Jumping Squares

Age 5 to 7 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

The Clockmaker's Birthday Cake

Age 7 to 11 Challenge Level:

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Rabbits in the Pen

Age 7 to 11 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

The Puzzling Sweet Shop

Age 5 to 11 Challenge Level:

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?

Magic Triangle

Age 7 to 11 Challenge Level:

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Magic Circles

Age 7 to 11 Challenge Level:

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Dice Stairs

Age 7 to 11 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

One Big Triangle

Age 5 to 7 Challenge Level:

Make one big triangle so the numbers that touch on the small triangles add to 10.

Fitted

Age 7 to 11 Challenge Level:

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Numbered Cars

Age 7 to 11 Challenge Level:

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Tricky Triangles

Age 5 to 7 Challenge Level:

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Starfish Spotting

Age 5 to 7 Challenge Level:

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

What's in a Name?

Age 5 to 7 Challenge Level:

What do you notice about these squares of numbers? What is the same? What is different?

Sliding Game

Age 7 to 11 Challenge Level:

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

Gift Stacks

Age 7 to 11 Challenge Level:

Use the information to work out how many gifts there are in each pile.

Two-digit Targets

Age 5 to 7 Challenge Level:

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Coded Hundred Square

Age 7 to 11 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Fractions in a Box

Age 7 to 11 Challenge Level:

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.

A Numbered Route

Age 7 to 11 Challenge Level:

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Strike it Out

Age 5 to 11 Challenge Level:

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Area and Perimeter

Age 7 to 11 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Fifteen Cards

Age 7 to 11 Challenge Level:

Can you use the information to find out which cards I have used?

Junior Frogs

Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Strike it Out for Two

Age 5 to 11 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Four-digit Targets

Age 7 to 11 Challenge Level:

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Oranges and Lemons

Age 7 to 11 Challenge Level:

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Make 100

Age 7 to 11 Challenge Level:

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Cycling Squares

Age 7 to 11 Challenge Level:

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

How Many Eggs?

Age 7 to 11 Challenge Level:

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Zios and Zepts

Age 7 to 11 Challenge Level:

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?

Sisters and Brothers

Age 7 to 11 Challenge Level:

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Rocco's Race

Age 7 to 11 Short Challenge Level:

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Let's Face It

Age 7 to 11 Challenge Level:

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

Magic Matrix

Age 7 to 11 Challenge Level:

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

The Brown Family

Age 5 to 7 Challenge Level:

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Find a Path

Age 5 to 7 Challenge Level:

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

One Wasn't Square

Age 7 to 11 Challenge Level:

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.

Domino Join Up

Age 5 to 7 Challenge Level:

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?