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Okay, I see your corrections. Now the problem is solvable.

Hi Mathegocart;

Also, there has to be more constraints put on a and b. Are they integers? Positive integers?

He should leave out the f(x). It has no meaning here.

It should be

2) 15. Let f(a,b) be defined as a^2+b^2-2, which of the following CANNOT be the value of f(a,b)?

(a) 0

(b) 2

(c) 3

(d) 6

Is it 2?

What kind of numbers are a and b? Integers? What other constraints are put on them?

Hi Mathegocart;

Any chance we can get some clarification on 2,3,8 and

Hi Zeeshan 01;

Could you explain a bit what you want?

Hi;

What is that after #8?

More like a combinatorics one. The King of math!

In the US there are 1 cent coins, 5 cent coins, 10 cent coins, 25 cent coins and 50 cent coins. A person goes to the store and hands the cashier 1 dollar ( worth 100 cents ). He asks her to change the dollar into coins.

One way for her to change his dollar into coins would be one 50 cent coin, one 25 cent coin, one 10 cent coin, one 5 cent coin and ten one cent coins. The math question is: how many ways can she give him change.

This is a pretty sophisticated math problem, many will be unable to answer, many more will be unable to compute the answer even if they could set it up. To even a beginning programmer this problem is trivial. A case of code being much easier than math.

There are many other such cases.

Hi;

https://www.mathsisfun.com/algebra/part … tions.html

They are used for lots of things but two things come to mind quickly, sums and integrals.

Yep, Principle of Inclusion Exclusion, PIE for short.

Welcome to the forum.

These double derangement or ( hat and coat ) problems are always a big pain in neck. The only analytical approach I know of is PIE and I do not use it.

Luckily these problems are rather well known so there is a formula and of course there is a direct computer count.