A mathematical puzzle from the Moscow Mathematical Olympiad 1983 has been presented by puzzle columnist Alex Bellos. The challenge is to find the smallest number N that begins with the digit 4. When the leading 4 is moved to the end of the number, the resulting number is exactly one quarter of the original N.
The Puzzle: Nose to Tail
Let N be a number starting with 4, such that if you take the 4 from the front and place it at the end, you get a new number that is N divided by 4. In other words, N is of the form 4[...], where [...] is a sequence of digits, and N divided by 4 equals [...]4. For example, if N were 45, then moving the 4 to the end would give 54, but 45 divided by 4 is 11.25, not 54. So that does not work.
Hint for Solving
The puzzle suggests trying different lengths for N. Start by assuming N has two digits. If no solution exists, try three digits, and continue until you find the smallest possible N. The solution is expected to be revealed at 5pm UK time.
Readers are encouraged to discuss the puzzle without spoilers. The puzzle is part of Alex Bellos's Monday puzzle series, which has been running since 2015. If you have a great puzzle to suggest, you can email the author.
