Can You Solve This Mathematical Puzzle? The Number That Begins and Ends with 4

AI Summary

This article presents a mathematical puzzle from the Moscow Mathematical Olympiad 1983, asking readers to find a number N that begins with 4 and when the 4 is moved to the end, the resulting number is exactly a quarter of N. The puzzle challenges mathematical reasoning and problem-solving skills.

The Mathematical Challenge

Today's offering is for fans of the number 4. It's a cute puzzle that offers up its solution in an elegant way.

Nose to Tail Problem

There is a number N beginning with 4 such that moving the 4 to the end of it creates a new number that is a quarter of N.

In other words N is of the form 4[…], where […] is a sequence of digits, and N ÷ 4 = […]4

What is the lowest possible value of N?

Problem-Solving Approach

HINT. Suppose that N has two digits. If you can't find a solution, suppose that N has three digits. Repeat until done.

I'll be back at 5pm UK with the solution.

PLEASE NO SPOILERS. Instead discuss snouts.

Solution and Sources

UPDATE: Solution is here.

Source: Moscow Mathematical Olympiad 1983, via @mathematicsproblems and Kevin Gately

Puzzle Column Information

I've been setting a puzzle here on alternate Mondays since 2015. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.