This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Given the products of diagonally opposite cells - can you complete this Sudoku?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Number problems at primary level that require careful consideration.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Can you work out some different ways to balance this equation?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of adjacent cells, can you complete this Sudoku?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Have a go at balancing this equation. Can you find different ways of doing it?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Four small numbers give the clue to the contents of the four
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?