Question 119
Leonard Larsson's Language
The linguist Leonard Larsson made up a new language in which all words have exactly seven letters and only the twenty letters from $A$ to $T$ are used. Furthermore, any pair of distinct words differ in at least two places. (For instance, if the words $LEONARD$ and $LARSSON$ are part of this language, then $LEOPARD$ and $PARSSON$ cannot be words.)
Leonard claims that if he needs more words, the language rules allow him to create more than $70$ million words. His colleague says “I presume you mean more than $60$ million words?”. Prove that indeed these rules allow for more than $60$ million words but not more than $70$ million.
The linguist Leonard Larsson made up a new language in which all words have exactly seven letters and only the twenty letters from $A$ to $T$ are used. Furthermore, any pair of distinct words differ in at least two places. (For instance, if the words $LEONARD$ and $LARSSON$ are part of this language, then $LEOPARD$ and $PARSSON$ cannot be words.)
Leonard claims that if he needs more words, the language rules allow him to create more than $70$ million words. His colleague says “I presume you mean more than $60$ million words?”. Prove that indeed these rules allow for more than $60$ million words but not more than $70$ million.