# Hard but easy

I solved some math problems of higher levels than mine today and found them to be easier than my current level problems. Is it true that some of the problems of higher levels are quite easier than that of the lower levels? Or is it just because this week's problems of the higher levels were quite simple for"me"?

Note by Maharnab Mitra
4 years, 8 months ago

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There are many reasons why a problem was rated higher, but could be easier to you. Here are a few:

1. Note also that just because it was assigned to a higher level student, doesn't necessarily mean it is considered harder than your problems. Each level receives problems from a range of difficulties, and there is overlap between two consecutive levels. You will not have seen all of their easy problems.

2. Of course, I could have assigned the problem wrongly. I would be foolish to claim that it never happens, especially since the difficulty of a problem is highly dependent on the individual.

3. The problem is a simple application of a complex technique. For example, a basic question on partial fractions might not be shown to level 1 students, but could easily done by anyone who has seen it, and even by those who merely guess at how it works without knowing the proper theory.

4. Problems which have subtle proofs could have a numerical answer that is easily guessed, but hard to actually demonstrate. For example, see my discussions Primes in a magic square and these roots have roots.

5. You might have seen a similar problem before, and recall the approach to solving it. That doesn't make the problem easier (to the community), though it makes it easier to you.

6. Making a calculator (or a program) do the work for you isn't considered solving the problem.

Staff - 4 years, 8 months ago

You can decide that by seeing the number of people who have solved the question. That would give you an idea whether the questions were easy or not. By the way, this happens with me as well sometimes!

- 4 years, 8 months ago