Problems
Teddy Bear Line-up
Stage:1 Challenge Level:
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
Let's Cut the Cake
Stage:1 Challenge Level:
How could Janus' birthday cake be cut into 8 equal pieces by making just three straight cuts?
Buying a Balloon
Stage:2 Challenge Level:
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Birthday Bewilderment
Stage:2 Challenge Level:
Can you explain what Janus means when she says that she was nine years old two days ago and she will be twelve next year?
Calendar Calculations
Stage:2 Challenge Level:
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
01012001
Stage:2 Challenge Level:
29th March 1987 (or 29.03.87) and 8th November 1988 (or 8.11.88) are special 'productive' dates because 29 x 3=87 and 8 x 11=88. Which year has the most 'productive' dates?
World of Tan - Millennia
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outlines of the workmen?
Calendar Capers
Stage:3 Challenge Level:
Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .
2001 Spatial Oddity
Stage:3 Challenge Level:
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
Slippy Numbers
Stage:3 Challenge Level:
The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
Small Change
Stage:3 Challenge Level:
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
Adding in Rows
Stage:3 Challenge Level:
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Rationals Between
Stage:4 Challenge Level:
Show that for all but two values of the integer q there is some integer p such that sqrt {56} < p/q < sqrt{58} and find these exceptional values of q.
Medallions
Stage:4 Challenge Level:
I keep three circular medallions in a rectangular box in which they just fit with each one touching the other two. The smallest one has radius 4 cm and touches one side of the box, the middle sized. . . .
In All Probability
Stage:4 Challenge Level:
A pack of 10 cards numbered from 1 to 10 is shuffled and dealt into two hands of 5 cards. What is the probability that the 8, 9 and 10 are all in the same hand?
Grid Points on Hyperbolas
Stage:5 Challenge Level:
Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.
After Thought
Stage:5 Challenge Level:
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Quartics
Stage:5 Challenge Level:
Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.
Elsewhere...
Featured Solutions
Articles & Games
Calendar Activities
Don't get rid of your old calendars! You can get a lot more mathematical mileage out of them before they are thrown away. These activities, using cut up dates from the calendar, provide numbers to practise skills that may be in need of review after a holiday break.
