This is a problem from the 2018 WSMC math competition, I was preparing for the competition this year and have no idea how to do this problem. Any help will be appreciated, thank you.
2026-03-30 12:22:50.1774873370
Either 1, 2, or 3 points can be scored from make a hoop in basketball, how many unique values of points can be generated from scoring 10 hoops?
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1
The maximum points which can be scored is equal to $30$. The minimum is $10$. When all the numbers are $1$ it will be equal to $10$ points. To score $11$ replace a $1$ with $2$, similarly to get $12$ replace another $1$. When all the $1$s are replaced by $2$ you get $20$. To score $21$ replace another $2$ with $3$ and proceed further to reach $30$. So all the numbers can be formed between $10$ and $30$. So the number of such numbers would be $21$.
Note: the question is asking to find number of values of points not the combination of scores. So don't confuse between the two.