When we write a (b + c) = ab + ac, everyone understands that, in this equation, the absence of a symbol between two letters denotes multiplication. Everyone will therefore agree that the only positive real number x satisfying the equation xx = 2 (more commonly written x2 = 2) is This is where matters become more complicated between Valentin Desgranges, a young student from Toulouse who attracted attention at the 2017 Mathematics Olympiad in the economics and social sciences stream, and a major retail chain operating in Hauts-de-France.
In late August 2018, the retailer posted the puzzle below on social media. The prize was a computer, a printer, a mouse and an Office software package.
Most entrants give 9 as their answer, but Valentin Desgranges treats each picture as representing an unknown number. This amounts to translating the puzzle into the following system (see the third equation):
Implicitly assuming that the value of a mouse is positive, he concludes that the expected answer is actually and considers himself the sole winner of the prize. The judge will hand down a ruling on 12 September.
The student's argument.
