Math Help - Spot the formula

1. Spot the formula

If I know a and b, is there a formula for c?

a b c
1 1 1
1 2 2
2 2 2
1 3 2
2 3 4
3 3 4

How do I 'spot the formula'?

thanks

2. Yes.
Any way you like.

3. Truthfully, there are infinitely many formulas that describe what you have given. Really, just pick one.

On this sort of problem, it probably is important to remember that the solution may not be mathematical at all.

Here is an example of "non-mathematical."

0 - 4
1 - 3
2 - 3
3 - 5
4 - 4
5 - 4
6 - 3
7 - 5

It's the number of letters in the word. o-n-e is three letters.

In my view, almost always, this kind of problem only just barely belongs in a math class. I think they are almost always busy work and a waste of time.

$\frac{3}{4} \cdot 4 \;=\; 3$ -- LaTeX Check

4. Here's one:

"c is the smallest integral power of two greater than or equal to the arithmetic mean of a and b."

5. Here's one:

a b c
1 1 1

1 2 2
2 2 2
1 3 2
2 3 4
3 3 4
1 4 4
2 4 4
3 4 4
1 5 8

The values in columns a and b mean nothing. The number of of powers of two simply increases by 2 for each phase.

Infinitely many. Just pick one. If someone argues with you, simply demonstrate it.