can you give me some puzzling questions in maths?

Question

can you give me some puzzling questions in maths i want to do a project on the basis of this.
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Answer 1

factor each.
a^2-(4a)+ab-4b
3b^3+b^2+6b+2
49q^2-28qm+4m^2-9m^2-36np-36p^2
proove that 2+0 ans.
suppose x and y are any real numbers.
x^2=y^2
x^2-y^2=0
2(x^2-y^2)=(2)(0)
2(x+y)(x-y)=0
2((x+y)=0
2=0

Answer 2

Here's one that's puzzled many of us for years:
Let n be a positive integer(in base 10) satisfying
a). n is a square
b). the only digits of n are 0 and 1
Must n be a power of 10?
A computer check reveals that the only "0-1 squares"
less than 10^36 are indeed powers of 10.


Another one you might want to look at is the
infamous 3x+1 problem.

Finally: The 3 cubes problem.
Find 3 integers, x,y,z such that x³+y³+z³ = 33.





















Fi

Answer 3

let P be a point inside an equilateral triangle of side d and has distances a, b, c from the vertices.
q1
if a, b, c are given, find d explicitly in terms of a, b, c.

q2
if b, c, d are given, find a explicitly in terms of b, c, d.

maybe not so hard for you, but i need the answer...please?