How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Can you find the ratio of the area shaded in this regular octagon to the unshaded area?

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

This problem looks at how one example of your choice can show something about the general structure of multiplication.

Find the sum of all three-digit numbers each of whose digits is odd.

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Use the interactivity or play this dice game yourself. How could you make it fair?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

Design your own scoring system and play Trumps with these Olympic Sport cards.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

To celebrate the 2016 Olympic Games, why not have a go at these maths and sport challenges?

Celebrate the 2016 Olympics by having a go at these sports and maths challenges for upper primary students.

Alan Parr offers some thoughts on various measurements recorded during the Olympic Games. From the accuracy of timing in the pool to the point system in the heptathlon, Alan gives us food for. . . .

These Olympic quantities have been jumbled up! Can you put them back together again?

Can you deduce which Olympic athletics events are represented by the graphs?

This problem is intended to get children to look really hard at something they will see many times in the next few months.

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Jenny Piggott reflects on the event held to mark her retirement from the directorship of NRICH, but also on problem solving itself.

You have 5 darts and your target score is 44. How many different ways could you score 44?

If you move the tiles around, can you make squares with different coloured edges?

A introduction to how patterns can be deceiving, and what is and is not a proof.

Four vehicles travelled on a road. What can you deduce from the times that they met?