Mathematical problem without a solution?

Question

a word problem that has no solution and why there no solution

Answer 1

different reasons for different problems

Answer 2

Problem:

Find the smallest number greater than 0.

If you take any number x>0, then 0<x/2<x so there is no smallest number  greater than zero. Thus this problem has no solution.

Answer 3

Here are two:

1) Susie has twice as many brothers as sisters.

Her brother Bobby has 3 times as many sisters as brothers.

How many kids in the family ?

Let b = boys, g = girls.

b = 2 (g - 1) = 2g - 2

g = 3 (b - 1) = 3b - 3

From second equation,

g = 3(2g-2) - 3 = 6g - 9

5g = 9, g = 9/5

From first equation,

b = 2(3b-3) - 2 = 6b-8

5b = 8, b=8/5

The family has 1 4/5 girls and 1 and 3/5 boys.

I don't think so! You cannot have "fractional kids".

A number cubed is the number multiplied by itself twice more:

2 x 2 x 2 = 8, 3 x 3 x 3 = 27.

Billy has a number of marbles which is some number cubed,

Joey has a number of marbles which is also a number cubed,

Jimmy has a number of marbles which is also a number cubed.

Jimmy has as many as Billy and Joey together.

How many does each one have ?

(No such numbers exist).

The above is an instance of a very famous problem called Fermat's Last Theorem:

Find numbers x, y, z, n such that

x^n + y^n = z^n (n > 2, neither x nor y = 0).

Over the course of 300 years it was proved that no such

numbers exist for many different values of n, but only

very recently was a general proof found.

.

Answer 4

Any problem, mathematical or not, must have a solution. Otherwise, it is not a problem. Just let it be.