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From the people behind the Alan Turing Cryptography Competition.
You are reading the website of the 2018 edition of the MathsBombe, which ended on Saturday 28th April at 11:59 pm

Puzzle 4.

A large University employs professors, lecturers and security guards. Each one of the ten thousand employees receives exactly the same salary, paid in cash on the first of the month. On every day of the month, one of the professors takes part of his or her cash and divides it equally among all the lecturers. Then a lecturer distributes part of his or her money equally among all the professors. No one gives cash to security guards or uses it in any other way.

At the end of the month, Professor Alice and Lecturer Bob were left with a thousand pounds in cash each, whereas Professor Chuck had only a pound and a penny, the same as Lecturer Dave. If there are more lecturers than professors, how many security guards work at the University?

Your answer:
No answers can currently be submitted as the competition is closed.
MathsBombe 2017 is organised by the The School of Mathematics at the University of Manchester.
Contact us via mathsbombe@manchester.ac.uk with any queries.