Label the boxes $1,2,\cdots 10$, by ascending number of pencils in the boxes. Choose an arbitrary pencil from box $1$. Then box $2$ contains a pencil which is distinct from the chosen pencil, so choose it next. box $3$ has at least $3$ pencils (from the condition that all boxes have distinct numbers of pencils), so has at least 1 distinct pencil form the chosen pencils, so choose it next. In general, once we reach box $i$, we have chosen $i-1$ pencils, and since box $i$ has at least $i$ pencils, we are able to choose a distinct pencil from it. Continuing this, we will get one pencil from each box, all distinct. Cheers, Rofler