The daughter of a relative of mine, a fifth-year school student in Russia, got the following math homework from her teacher:
Here's my translation:
No. 26. Students were solving a task in which they had to figure out the missing numbers:
They came up with different answers:
Find the rules used by the students to fill out the squares, and come up with a fourth solution.
Explaining the first two solutions is easy. In the first solution, the student assumed that in each horizontal line, the sum of the first two numbers equals the third one. In the second solution, the student assumed that the difference between the numbers in each vertical row is the same.
The girl couldn't explain the third diagram and asked her parents, who then asked me. Unable to help them, I'm posting this question.
My question: Is there a logical explanation of the third solution?
Looking at the third solution, I noticed that the numbers in each horizontal line add up to the same number, 80, but how could one get 80 from the original diagram in the first place? Also, the digits in each horizontal line add up to the same number, 17, but, again, how could one get 17 in the first place? It seems I stumbled upon false leads.
Being a professional physicist, I feel ashamed to tell the girl's parents that I can't solve the problem. I find it likely that the teacher made a mistake in the third diagram, but I'm afraid to bet on that possibility, so I hope you can suggest a valid logical explanation of the third diagram and thereby help me save my face.