What is the hardest math question?

Answer 1

If only international or American questions,

1. IMO

2. USA TST

3. Putnam

4. USAMO

Another Answer:

Three men went to a hotel to rent a room, the cost of the room was $30. Each man paid $10 to the bellboy and proceeded to their room. After a little while the bellboy realized that there was a special on rooms that night and the price for the men's room should have been $25. On his way to the men's room to give them back $5, he was puzzled how he was going to split $5 as he had no change. He decided he would give them each $1 and keep the remaining $2 for himself. So each man originally paid $10, but after the bellboy gave each man $1 back, each man paid $9. 9 x 3 = $27 plus the $2 the bellboy put in his pocket equals $29. The original price for the room was $30. Where did the last dollar go?

Which shows that even though something sounds logical, it might not be. There is no "last dollar". There is a fallacy in the thought process and calculations. The $2 should be subtracted from the $27 to show what ended up being paid for the room. Or

$30 - $1 - $1 - $1 - $2 = $25

Another Answer:

Probably the most difficult recently solved problem was Fermats enigama, which involved cubes. It has taken many years and the consolidation of the work of dozens of people to resolve.

Another Answer:Information required to complete the questionYou are given a triangle that has sides of 66cm, 73cm, and 94cm. One of the angles is right-angled (meaning that it is possible by trial and error to calculate what each of the angles are). Inside this triangle is a square, so that three corners are in contact with the lines bounding the triangle. One of the sides or the square, which we shall now dub z, is also tangent to a circle, with a radius such that the centre of the circle lies along the side of the triangle with length 73cm. You are also given a regular octagon, which you are told is the same area as the total are of the circle and triangle if they are taken together (i.e. the overlapping area is not counted twice), and one side of this octagon forms another side of equal length belonging to a second square. The area of this square is dubbed x. Part 1Give the value, to three significant figures, of x.

[15 marks]

Part 2An isosceles triangle is drawn so that it has the same area as the above square (i.e. x), and with two sides that are equal to the square root of x (henceforth dubbed y). What is the length of the third side?

[100+90-7685*58/92 marks]

Part 3Prove that the triangle above exists.

[25 marks]

Part 4What is the area of a octagon of side length y, in cubic inches. (Note that this question uses non-euclidean goemetry)

[2Ï€r marks]

Part 5Through cunning use of Pythaogoras' Theorem, prove that aliens do not exist.

[-0 marks]

Part 6If , then what does y smell like?

[-10 marks]

Part 7What is the answer of this question?
Tensor calculus may be the most difficult non esoteric branch of mathematics. Multivariate differential vector calculus may sound scary, but most folks can solve problems of this nature with just a little bit of training. Your cat solves problems like these every time she pounces on a bird.

But what are tensors? Are these more generalized concepts of vectors? And are there imaginary tensors? Inquiring minds want to know.