Poly Plug Rectangles
Age 5 to 11 Challenge Level:
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Dozens
Age 7 to 14 Challenge Level:
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Reach 100
Age 7 to 14 Challenge Level:
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.
Odds, Evens and More Evens
Age 11 to 14 Challenge Level:
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Tilted Squares
Age 11 to 14 Challenge Level:
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Magic Letters
Age 11 to 14 Challenge Level:
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Shifting Times Tables
Age 11 to 14 Challenge Level:
Can you find a way to identify times tables after they have been shifted up or down?
Summing Consecutive Numbers
Age 11 to 14 Challenge Level:
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Polygon Rings
Age 11 to 14 Challenge Level:
Join pentagons together edge to edge. Will they form a ring?
Unequal Averages
Age 11 to 14 Challenge Level:
Play around with sets of five numbers and see what you can discover about different types of average...
Cyclic Quadrilaterals
Age 11 to 16 Challenge Level:
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Charlie's Delightful Machine
Age 11 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Pair Products
Age 14 to 16 Challenge Level:
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Steel Cables
Age 14 to 16 Challenge Level:
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Factorising with Multilink
Age 14 to 16 Challenge Level:
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Hollow Squares
Age 14 to 16 Challenge Level:
Which armies can be arranged in hollow square fighting formations?
Odds and Evens Made Fair
Age 14 to 16 Challenge Level:
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.