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jamesnulty
09-03-2015, 10:30 AM
Since there are so many mathematicians on here, can you confirm for me my thoughts about my 8 year old daughter's homework? I think she was set an impossible problem.

First the easy bit: simple addition practice. Imagine a square split into four smaller squares. She had to put 4 different numbers (1-9 only) in each square, then add up the four double digit numbers.

e.g.

19
23

19 + 23 + 12 + 93 = 147

She was then asked to fill the squares (with 4 different numbers) so that the total is 100. And the funny bit: see how many ways you can do it.

Well I don't think you can do it at all. And there is some logic behind my assertion.

Good luck!

dsr
09-03-2015, 10:47 AM
12
47

12 + 47 + 14 + 27 = 100

There may well be other solutions, I haven't looked for the logic.

[Edit] I think 2138 might be the only other one, plus rotations.

Number the boxes
ab
cd

The total will be 20 x a, 11 X b, 11 X c, 2 X d.

That means, ignoring the tens, that b+c+2d has to total 0 or 10 or 20 or 30. Work from there, using all 9 possible options for d. Only 2 of them work.

jamesnulty
09-03-2015, 10:57 AM
Oh dear - my daughter is going to be really embarrassed at school now.
Thank you for the enlightenment!

Notrigsbyscat
09-03-2015, 11:10 AM
Your Daughter!! :? :?

You're the one that said you didn't think it could be done!

jamesnulty
09-03-2015, 11:54 AM
I AM embarrassed, but what I meant is that I've caused her embarrassment by telling her it couldn't be done.
Lesson: don't try doing maths on a Sunday afternoon after a boozy lunch