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My 8 year old son came asking me to help with his homework and was given the following question. I think I am usually good at math but I don't see any pattern here.

  1. Label the two circles of the Venn Diagram according to the sorting rule that was used.

(Note there weren't any rules given for this question. However, some other unrelated patterns were used for other Venn diagrams such as greater than less than, odd or even in the same lesson).

enter image description here

  1. Add these numbers to the Venn Diagram 11, 4369.

Can anyone explain what is so simple that I and my son are missing here?

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  • $\begingroup$ 2-digit vs 3-digit numbers? $\endgroup$ – Don Thousand Oct 15 '18 at 1:26
  • $\begingroup$ What about question two? That wouldn't fit. I mean you could say numbers with two digits vs numbers with more than three. Unless the second question doesn't fit and it is a trick question. $\endgroup$ – jwize Oct 15 '18 at 1:26
  • $\begingroup$ It's probably some semi-arbitrary rule like "numbers less than 100 to the left" or "numbers that end in 3, 5, 9" to the left. $\endgroup$ – Fabio Somenzi Oct 15 '18 at 1:55
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To start, I'm fairly sure the answer is "less than 100 on the left, more than 100 on the right". It's the simplest rule that works.

However, it's not the only rule that works. As @Fabio Somenzi suggests in the comments, it could be "numbers that end in 3, 5, or 9 on the left, other numbers on the right". Alternatively, since Venn diagrams allow entries outside either circle, it could be "two digit numbers on the left, three digit numbers on the right", and then 4369 goes outside both circles. Or it could be "numbers that leave remainder 1, 2, or 3 when divided by 6 on the left, others on the right". And there are an infinite number of other rules that could work.

All in all, it's not a very good mathematics question: there are multiple answers that fit the information, and yet you are asked for "the" rule that was used, which suggests you are expected to find the "simplest" rule that works, for some not-fully-defined definition of "simplest".

But of course in many other fields - some not that far from mathematics - questions that want an answer that not only fits the data, but is also the most plausible answer that fits the data, are common, indeed central, at every level of study. So if the lack of certainty in the question is annoying you, think of it as, say, "data science for 8 year olds" rather than mathematics (strictly defined)!

That said, if you give an answer that works for part (1), and then correctly follow it through for part (2), it ought to be marked correct (though I can't guarantee that a teacher that sets this kind of question would do so).

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