List

Working Systematically

If you work systematically you can be sure you won't leave out any possibilities and it's a valuable skill for tackling many problems.  Have a go at these ...

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?

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

A Mixed-up Clock printable sheet

Here is a clock face where the numbers have become all mixed up. In the picture, each of the numbers is represented by a letter. Can you find out which letter represents which number using the ten statements below?

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A Mixed-up Clock
  1. No even number is between two odd numbers.
  2. No consecutive numbers are next to each other.
  3. The numbers on the vertical axis (a and g) add to $13$.
  4. The numbers on the horizontal axis (d and j) also add to $13$.
  5. The first set of $6$ numbers (a, b, c, d, e, f) add to the same total as the second set of $6$ numbers (g, h, i, j, k, l).
  6. The number at position f is in the correct position on the clock face.
  7. The number at position d is double the number at position h.
  8. There is a difference of $6$ between the number at position g and the number before it (f).
  9. The number at position l is twice the top number (a), one third of the number at position d and half of the number at position e.
  10. The number at position d is $4$ times one of the numbers next to it.

 

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?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Sealed Solution printable sheet

Here is a set of ten cards, each showing one of the digits from 0 to 9:

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Sealed Solution

The ten cards are divided up between five envelopes so that there are two cards in each envelope.

The sum of the two numbers inside it is written on each envelope:

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Sealed Solution

What numbers could be inside the "8" envelope?

Thank you to Alan Parr who inspired this task.

These activities ask you to find all possible solutions.  If you work in a systematic way, you will be sure not to leave any out!
Beads and bags
problem
Favourite

Beads and bags

Age
5 to 11
Challenge level
filled star empty star empty star
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Half Time
problem
Favourite

Half Time

Age
5 to 11
Challenge level
filled star empty star empty star
What could the half time scores have been in these Olympic hockey matches?
Buying a Balloon
problem
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Buying a Balloon

Age
7 to 11
Challenge level
filled star empty star empty star
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?
Fifteen cards
problem
Favourite

Fifteen cards

Age
7 to 11
Challenge level
filled star empty star empty star
Can you use the information to find out which cards I have used?
Cubes Here and There
problem

Cubes Here and There

Age
7 to 11
Challenge level
filled star empty star empty star
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Trebling
problem
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Trebling

Age
7 to 11
Challenge level
filled star empty star empty star
Can you replace the letters with numbers? Is there only one solution in each case?
Factor Lines
problem
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Factor Lines

Age
7 to 14
Challenge level
filled star filled star empty star
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Sealed Solution
problem
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Sealed Solution

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Magic Vs
problem
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Magic Vs

Age
7 to 11
Challenge level
filled star empty star empty star

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

All the Digits
problem
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All the Digits

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Finding Fifteen
problem
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Finding Fifteen

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Button-Up Some More
problem
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Button-Up Some More

Age
7 to 11
Challenge level
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How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This Pied Piper of Hamelin
problem
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This Pied Piper of Hamelin

Age
7 to 11
Challenge level
filled star filled star empty star

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Reach 100
problem
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Reach 100

Age
7 to 11
Challenge level
filled star filled star empty star

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.

5 on the clock
problem
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5 on the clock

Age
7 to 11
Challenge level
filled star filled star filled star
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?
Nine-Pin Triangles
problem
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Nine-Pin Triangles

Age
7 to 11
Challenge level
filled star empty star empty star

How many different triangles can you make on a circular pegboard that has nine pegs?

Inky Cube
problem
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Inky Cube

Age
7 to 14
Challenge level
filled star filled star filled star

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?

Having an ordered way of going about these activities will really help.  This might mean using the information given in a particular order or perhaps approaching the task in a methodical way which reveals patterns, helping you reach a solution.
Sitting round the party tables
problem
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Sitting round the party tables

Age
5 to 11
Challenge level
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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A Mixed-up Clock
problem
Favourite

A Mixed-up Clock

Age
7 to 11
Challenge level
filled star empty star empty star

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?

What Do you Need?
problem
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What Do you Need?

Age
7 to 11
Challenge level
filled star empty star empty star
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
A Square of Numbers
problem
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A Square of Numbers

Age
7 to 11
Challenge level
filled star empty star empty star
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Light the Lights Again
problem
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Light the Lights Again

Age
7 to 11
Challenge level
filled star filled star empty star

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Prison Cells
problem
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Prison Cells

Age
7 to 11
Challenge level
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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?
Two Primes Make One Square
problem
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Two Primes Make One Square

Age
7 to 11
Challenge level
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Can you make square numbers by adding two prime numbers together?
Tea Cups
problem

Tea Cups

Age
7 to 14
Challenge level
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Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Counting Cards
problem
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Counting Cards

Age
7 to 11
Challenge level
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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?
Curious number
problem
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Curious number

Age
7 to 11
Challenge level
filled star filled star filled star

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Make 37 Poster
problem
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Make 37

Age
5 to 11
Challenge level
filled star filled star empty star

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

First Connect Three
problem
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First Connect Three

Age
7 to 11
Challenge level
filled star empty star empty star
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?