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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 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.
How do you make a test conjecture with the product of two odd integers?
One possible conjecture is that the product of two odd integers is 8. A conjecture does not have to be true, nor does it have to be sensible. It must be testable, though. Many conjectures were initially thought to be sensible and true but later proven to be false. And when the false nature is fully understood, in retrospect they no longer appear sensible either!
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.
