Resources tagged with: Counting

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There are 23 results

Broad Topics > The Number System and Place Value > Counting

Amazing Card Trick

Age 11 to 14 Challenge Level:

How is it possible to predict the card?

Adding with the Abacus

Age 5 to 16

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?


Age 11 to 14 Challenge Level:

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

Nim-7 for Two

Age 5 to 14 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Card Trick 2

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

Slippery Snail

Age 7 to 16 Challenge Level:

A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.

Diagonal Sums Sudoku

Age 7 to 16 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.


Age 5 to 14 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second?

FEMTO: Follow Up

Age 14 to 16 Challenge Level:

Follow-up to the February Game Rules of FEMTO.


Age 14 to 16 Challenge Level:

A new card game for two players.

Back to the Planet of Vuvv

Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Ways of Summing Odd Numbers

Age 11 to 14

Sanjay Joshi, age 17, The Perse Boys School, Cambridge followed up the Madrass College class 2YP article with more thoughts on the problem of the number of ways of expressing an integer as the sum. . . .

Binomial Coefficients

Age 14 to 18

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.


Age 14 to 16 Challenge Level:

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

An Investigation Based on Score

Age 11 to 14

Class 2YP from Madras College was inspired by the problem in NRICH to work out in how many ways the number 1999 could be expressed as the sum of 3 odd numbers, and this is their solution.

Links and Knots

Age 14 to 18

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.


Age 11 to 14 Challenge Level:

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

How Many Dice?

Age 11 to 14 Challenge Level:

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

Cube Paths

Age 11 to 14 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Painting Cubes

Age 11 to 14 Challenge Level:

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Euler's Officers

Age 14 to 16 Challenge Level:

How many different ways can you arrange the officers in a square?

Voting Paradox

Age 14 to 18 Challenge Level:

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?