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What is an example of a TRUE conjecture?
The Poincaré Conjecture.
What conjecture can you make about the sum of the first 10 positive even numbers?
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
Make a conjecture about the sum of the first 25 positive even numbers?
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.
What is a conjecture about the number of factors for square numbers up to 1000?
One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.
What would be a conjecture of two consecutive exterior angles?
There is no logical conjecture that can be made for what could be an irregular polygon with an unknown number of sides. Of course, you could always conjecture anything. For example, that they will taste of strawberries. A conjecture that, I guess, will be disproved quite easily.
