Weekly Problem 18 - 2008

The diagram shows a regular pentagon. Can you work out the size of the marked angle?

Resources to accompany NRICH team presentations at UKMT 2012 Teacher Meetings.

Resources to accompany NRICH team presentations at UKMT 2013 Teacher Meetings.

Resources to accompany NRICH team presentations at UKMT 2014 Teacher Meetings.

Resources to accompany NRICH team presentations at UKMT 2015 Teacher Meetings.

Resources to accompany NRICH team presentations at UKMT 2016 Teacher Meetings.

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

This article explores the process of making and testing hypotheses.

Deepen your understanding of different types of information with these challenges.

Deepen your understanding of different types of information with these upper primary challenges.

These lower primary challenges focus on different types of information.

The problems in this feature encourage students to consider inverses and working backwards to solve problems.

Play around with sets of five numbers and see what you can discover about different types of average...

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

Is the sum or difference of two uniform random variables uniform?

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Invent shapes with different numbers of stable and unstable equilibrium points

This challenge is about finding the difference between numbers which have the same tens digit.

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

Can you prove our inequality holds for all values of x and y between 0 and 1?

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Can you work out the natural time scale for the universe?

A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

What is the perimeter of this unusually shaped polygon...

This quadrilateral has an unusual shape. Are you able to find its area?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Play this game to learn about adding and subtracting positive and negative numbers

Although almost any NRICH activity could be tackled in a group, these upper primary activities have been created specifically with group work in mind.

Activities for upper primary children which focus on working systematically.

The archive of our upper secondary student articles.

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

Read the book 'Maisy Goes Camping' by Lucy Cousins. Act out the story with some toys - is there room for one more in the tent? How many characters are in the tent now?

Read the book 'The Doorbell Rang' by Pat Hutchins. Have a go at sharing out some cookies like the characters in the story!