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In a chess tournament were played 105 games. Each chess player has played with every other player. How many chess players were at the tournament?

I have no clue how to solve this problem. I think this is a combination problem but don't know what formula to apply.

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    How many games are played in a tournament with $n$ players? I guess $\binom{n}{2}$. And $\binom{n}{2}=105$ implies $n=15$. – 2017-02-09
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    @JackD'Aurizio you used the combination formula, right? Could you please explain the algebra how you did it? – 2017-02-09
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    In general, if your approach to math is to ask yourself "what formula should I have to apply here?" you will probably have a hard time. It is more wise to ask yourself "what this problem really wants from me? What do I know? How can I fill the void between the starting point and the arrival?". Doing math is not really about applying formulas. It is dealing with ideas and abstract structures. Formulas are just a by-product. – 2017-02-09

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The missing ingredient is that each player played each other player exactly once. The problem should have said that.

OK, then if there were $n$ players, how many pairs of players could you make -- because each of those pairs necessitates exactly one game.

The number of pairs for $n$ objects is $\binom{n}{2} = \frac{n(n-1)}{2}$ Solving $$ \frac{n(n-1)}{2}=105\\ n^2 - n - 210 = 0 $$ we get $n=15$ (or $n=-14$, which is obviously not realistic). So there were $15$ players in the tournament.

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    This was a question in a university entrance exam, they missed that ingredient in purpose i suppose – 2017-02-09