Unbiased random number generator

Question

we have a six-sided dice numbered from 1 to 6, and each has the probability $p =\frac{1}{6}$. My task is to create a unbiased method to generate a random number from 1 to 10 using the given dice. I am aware that the method should maps the following set $$ \{1,\dots 6\}^k\mapsto \{1,\dots, 10\}$$, with $k$ is the number of time we throw the dice. For sure not the 36 elements will be mapped into the set containing 1 to 10. What i mean, the method will use a while loop and only stops if a certain tuple is found. My task then is the find those tuples and prove each thoese 10 tuples has the probaitly of $\frac{1}{10}.$ I think $k$ should be 2 in this case , but then i am not quite sure how to extract the 10 elements from 36 elements ($6^k$,with $k=2$) and have a probability of $p'=\frac{1}{10}$. can we maybe also generalize that for$ n$ elements ?

$$ \{1,\dots 6\}^k\mapsto \{1,\dots, n\} $$ I will appreciate any good ideas.