Stage: 3 Challenge Level: 
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
Working systematically. Addition & subtraction. Common factors. Divisibility. Modulus arithmetic. Factors and multiples. smartphone. Multiplication & division. Workshop. Properties of numbers.
Published December 2001,January 2002.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk