Simon is obsessed with Euclidea https://www.euclidea.xyz/ — a learning environment for geometric constructions and proofs. He has also downloaded the Euclidea app (which has more features), so that he could continue engaging with it while at the beach.

Yesterday, he finished the whole first section (called Alpha), completing all of its 7 tasks in several ways, most of which he solved himself without using hints. The goal is to solve a problem using the minimum number of moves:

Each solution is scored in two types of moves: L (straight or curved lines) and E (elementary Euclidean constructions). Points are not taken into account.

L counts tool actions: constructing a line, a perpendicular, and so on.

E counts moves as if a construction was made with real compass and straightedge. (Each advanced tool has its own E cost).Each level has L and E goals. They are independent. A lot of problems have universal solution that satisfies both goals. But some problems should be solved twice: one solution to reach L goal and another solution to reach E goal.

You can receive the following stars on each level:

* the challenge was solved

* the L goal was reached

* the E goal was reached

* all variants (V) of answer were foundIf there are several objects satisfying the statement of a problem, you can get a hidden V-star by constructing all the answers (solutions) at the same drawing. Usually this implies some kind of symmetry. You need to guess on what levels it is possible because the presence of a V-star is not shown until you find it.

– Euclidea Manual

The five images below are an example of solving a Euclidea puzzle:

Simon also loves recreating all the puzzles:

For the last puzzle, Simon couldn’t find the minimum number of moves independently and looked the solution up on stackexchange. “It would have taken me a year to figure this out”, he said: