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#### Resources tagged with Trial and improvement similar to How Many?:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Trial and improvement

### Four Colours

##### Stage: 1 and 2 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.

### Dice Stairs

##### Stage: 2 Challenge Level:

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

### Cycling Squares

##### Stage: 2 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?

### The Brown Family

##### Stage: 1 Challenge Level:

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

### One Million to Seven

##### Stage: 2 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

### One Big Triangle

##### Stage: 1 Challenge Level:

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

### Difference

##### Stage: 2 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.

### Tricky Triangles

##### Stage: 1 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?

### Find the Difference

##### Stage: 1 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.

### Twenty Divided Into Six

##### Stage: 2 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?

### Rocco's Race

##### Stage: 2 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.

### Fractions in a Box

##### Stage: 2 Challenge Level:

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

### Three Cubed

##### Stage: 2 Challenge Level:

Can you make a 3x3 cube with these shapes made from small cubes?

### Arranging the Tables

##### Stage: 2 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.

### Sliding Game

##### Stage: 2 Challenge Level:

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

### Magic Circles

##### Stage: 2 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?

### Strike it Out

##### Stage: 1 and 2 Challenge Level:

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

### Coded Hundred Square

##### Stage: 2 Challenge Level:

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

### A Shapely Network

##### Stage: 2 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.

### Rabbits in the Pen

##### Stage: 2 Challenge Level:

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

### Sports Equipment

##### Stage: 2 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

### Jumping Squares

##### Stage: 1 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.

### Junior Frogs

##### Stage: 1 and 2 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?

### The Puzzling Sweet Shop

##### Stage: 2 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?

### Strike it Out for Two

##### Stage: 1 and 2 Challenge Level:

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

### All Change

##### Stage: 1 Challenge Level:

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

### Prison Cells

##### Stage: 2 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?

### Fifteen Cards

##### Stage: 2 Challenge Level:

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

### Tubular Path

##### Stage: 2 Challenge Level:

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

### Area and Perimeter

##### Stage: 2 Challenge Level:

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

### Paw Prints

##### Stage: 2 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?

### Fitted

##### Stage: 2 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

##### Stage: 2 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?

##### Stage: 1 Challenge Level:

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

### Grouping Goodies

##### Stage: 1 Challenge Level:

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

### Five Steps to 50

##### Stage: 1 Challenge Level:

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

### Path to the Stars

##### Stage: 2 Challenge Level:

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

### Factor-multiple Chains

##### Stage: 2 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

### A Numbered Route

##### Stage: 2 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?

### Escape from the Castle

##### Stage: 2 Challenge Level:

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

### Four-digit Targets

##### Stage: 2 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?

### The Tall Tower

##### Stage: 1 Challenge Level:

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

### Number Round Up

##### Stage: 1 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.

### Two-digit Targets

##### Stage: 1 Challenge Level:

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

### Inky Cube

##### Stage: 2 and 3 Challenge Level:

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?

### Spiders and Flies

##### Stage: 1 Challenge Level:

There were 22 legs creeping across the web. How many flies? How many spiders?

### Number Juggle

##### Stage: 2 Challenge Level:

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

### Zios and Zepts

##### Stage: 2 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?

### Pizza Cut

##### Stage: 2 Challenge Level:

Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

### What Two ...?

##### Stage: 2 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers?