Last month, British student Alex Chui became the all-time most successful contestant at the International Mathematical Olympiad.<\/p>\n
Chui, a year 13 student at Tonbridge School in Kent, scored 100 per cent in this year\u2019s event, held in Shanghai, winning him a gold medal, and bringing his tally of medals to seven, five of them golds.<\/p>\n
No other contestant in the history of the IMO, which has been running since 1959 and brings together school-age contestants from more than a hundred countries, has won a medal seven years in a row.<\/p>\n
I asked Alex if he had a favourite puzzle, and he suggested the following gem.<\/p>\n
How many ways are there to fill a 3\u00d73 grid with positive whole numbers such that the product of the numbers in each row and each column is 30?<\/p>\n
[Each of the nine cells in the grid has a whole number in it. When you multiply the three numbers in each row, and in every column, the answer is 30. The three numbers in each row or column do not have to be three different numbers.]<\/p>\n
It\u2019s a very elegant puzzle. Your first instinct might be to try to count the completed grids individually. But that will take you a while, since it can be done in more than 200 ways.<\/p>\n
I will reveal his solution to you at 5pm UK today.<\/p>\n
PLEASE NO SPOILERS Instead discuss grids.<\/p>\n
The IMO takes place every year, and is held over two days. Each day is a four and a half hour exam with three questions, each worth seven points. This year is the first that Chui \u2013 who will study maths at Cambridge next term \u2013 scored 42\/42.<\/p>\n
I\u2019ve been setting a puzzle here on alternate Mondays since 2015. I\u2019m always on the look-out for great puzzles. If you would like to suggest one, email me.<\/p>\n