March 2006
Shapes
The diagram shows three pentominoes which have been placed on a grid. (A pentomino is a shape which can be formed from five adjacent squares.)
The pentominoes occupy only the white cells in the grid, not the grey ones. They do not touch each other, not even diagonally at a corner.
The numbers around the edge of the grid show how many squares in that row or column form part of a pentomino.
There are twelve different pentominoes. Find all of them.
The twelve pentominoes can be placed on the grid below according to the rules above. Can you work out how to do it?
Numbers
The diagram shows two calculations. The numbers in each column are identical.
The diagram below shows six calculations. Fill in the numbers 1 to 9 in the un-shaded boxes so that all the calculations are correct. The numbers in each column should be identical. You must use all of the numbers from 1 to 9.
Algebra
The multiplication sum 23 × 64 = 1472 is unusual because if we reverse the order of the digits in the two two-digit numbers we get 32 × 46, but the answer is still 1472.
Find all the two-digit multiplication sums which work in this way.
If you can’t work out a way to find them all, find as many as you can.
(Hint: The same technique that was used for the January and February puzzles will work again here.)
Miscellaneous
The diagram shows a ‘double sudoku’. Each row, each column, and each two by two square must contain the numbers 1 to 8. Each box will contain two numbers. No two boxes may contain the same combination of two numbers. (For example, no other box may contain 1 and 7.)
Can you complete the puzzle?