You may move straight to the solution and skip the following section on the brute-force approach.Īn idea on the brute-force approach to solution of 10 digit number puzzle by ConwayĪs an example, first two digits may be-12,14,16, 18 or 10 for the two digit number formed to be divisible by 2 (or an even number).Īnd for each of these combinations say 12, possible 3 digit numbers would be-123, 125, 127 or 129-a total of 20 possible combinations. Would you try out combinations of 10 digits for each place starting from left, test the divisibility for the place and move ahead without deeper analysis and using any faster systematic method?

How would you approach solving the puzzle? Solution to the 10 digit number puzzle of Conway If you try to solve the puzzle, you would enjoy the solution more. Our solution should be among the simplest as far as math used is concerned. And take your time to solve before seeing the solution.īeing a classic math puzzle, there can be other ways to arrive at the solution. Each of the digits is different, and,Ĭlarification: Each of the 10 numbers such as abcdefgh is not a product of the digits, it is a number formed by appending the digits one after the other from left to right. The 10 digit number puzzle of Conwayįind the 10 digit number, abcdefghij. It can be a rich source of learning in middle schools on how to form gradually growing restrictive patterns by basic divisibility rules for 0, 2, 3, 4, 5, 6, 8 and 9 and reasoning. Unless approached systematically, the puzzle may be found hard to solve, though practically anyone can solve this puzzle by systematic pattern finding reasoning. In our solution we have used math concepts at the middle school level, but we have also used Problem Solving Techniques and Mathematical reasoning. You may explore more about this 10 digit number puzzle and the creator John Horton Conway, the legendary playful genius of a mathematician with the fortunate streak of bringing fun into math that can literally be enjoyed by all.

To find such a 10 digit number from 3265920 possible 10 digit numbers is not easy, but is not too difficult also. Step by step solution by basic math explained. Find the 10 digit number, the beautiful math puzzle by Conwayįind the 10 digit number with each digit different and each number formed by first n digits divisible by n.

Riddle school 3 a10