article
Search for structure: actions and objects
John Mason describes the thinking behind this month's tasks.
Search
problem
Get cross
14 to 16
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
problem
Squaresearch
14 to 16
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
problem
Favourite
Caterpillars
5 to 7
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
problem
Pairs
11 to 14
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 thinking of.
problem
Favourite
More twisting and turning
11 to 16
It would be nice to have a strategy for disentangling any tangled ropes...
problem
Favourite
Crossed ends
11 to 14
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
game
Shut the box for two
5 to 7
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
problem
Sisters and brothers
7 to 11
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?