October 2005
Shapes
The diagram shows a large square containing a 7 by 7 grid.
Can you show how to divide this square into 7 right-angled isosceles triangles, no two of which are the same size? All vertices of the triangle must lie on the intersections of the grid.
Numbers
Fit the numbers from 1 to 16 into the table below so that each number is used once, and all the numbers in each row and column are as described. For example, the number in the box marked with a star (*) must be greater than 12 and a prime number.
| Square number | Prime number | Multiple of 3 | Factor of 280 | |
| Factor of 120 | ||||
| Greater than 12 | * | |||
| Even | ||||
| Odd |
Algebra
I am thinking of three numbers, all different. The sum of all three numbers is eight times the smallest number. The sum of the largest number and the smallest number is three times the middle number. How many times larger than the smallest number is the largest number?
Show how you worked this out.
Miscellaneous
In this ‘cross sum’ puzzle, each square should contain a digit from 1 to 9 (no 0s).
Each group of numbers going across has to add up to the number in the blue triangle to the left, and each group of numbers going down has to add up to the number in the green triangle above.
No digit can be repeated within a group. For example, the group of three digits going across the bottom row could not be 1, 3, 3 or 3, 1, 3 even though the digits in these groups add up to 7, because the group cannot contain two 3s.
Can you use logic to solve this puzzle?