A double-sided triangle, the math puzzle of “Le Monde” No. 63

While reading their newspapers, Sofia and Lubna came across the weekly math puzzle. One figure depicts a triangle with six squares, three of which are filled with numbers. Unfortunately, Sofia spilled her coffee on the page, and the wording is illegible.

"It's not a problem," says Lubna. "I know this game: you have to fill in the three missing squares so that each number is the sum of the two numbers below it. Except for the numbers in the bottom row, of course, which have nothing below them."

Can you fill in the three missing boxes according to Lubna's rule?

"Oh no!" replies Sofia. "I've seen a game like this before. Each number must be equal to the product of the two numbers below it!"

Can you fill in the three missing boxes according to Sofia's rule?

The next day, Lubna bursts into the breakfast table, triumphant, brandishing a sheet of paper scribbled with equations.

“I found it!” she announces.

– Found what? Sofia replies.

– The triangle to reconcile us.

In a corner of the draft, she points to a triangle of six numbers arranged like those in the newspaper puzzle. However, the numbers written there are all different. Sofia watches it for a few moments.

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