Problems & Puzzles: Puzzles
Puzzle 270. Euclidean questions
Stuart Gascoigne recall our attention to a puzzle original by G.P. Jelliss (The Games & Puzzles Journal, Issue 27)
Discussing the Euclid argument for the infinitude of the prime numbers, GPJ poses several questions, the 4th of them says:
Stuart Gascoigne has solved this question (he has found one solution) through a very clever semi-theoretical approach.
Moreover, he has solved also a close related but new question:
For this case he has found three non-trivial solutions .
1) Can you
rediscover the Gascoigne solutions to both questions?
Question 1 was solved by Faride Firoozbakht, Jon Wharf, Luke Pebody, Johann Wiesenbauer and J. K. Andersen. Nobody found more solutions than the previously found by Stuart Gascoigne. So the question 2 is still open.
The method used by the solvers is the same. Let's see the Pebody explanation: