word problem - Uncle Mort's Idiots

Uncle Mort was dead. Samuelson, the family lawyer, read the will. It stated that since he had no children of his own, his whole estate was to be divided between his two nieces, Roseanne and Chelsea and his nephew Sean if they "could demonstrate a semblance of co-operation and intelligence" by opening the combination safe in his office. They would have one chance. If they failed, the entire estate would go to charity. If they all agreed not to try, 90% of the estate would go to charity and they could split the remainder for "at least being smart enough to realise they are idiots."

Sean said: "10% is good. Let's take it." Roseanne agreed.

Chelsea had a question: "Can I, like, ask my boyfriend? He's so smart it's like weird or something."

Samuelson examined the will. "There is no provision for that. I will stretch a point and allow it. Go ahead, young man."

The safe had buttons on the front numbered 1 to 100. To open it, three buttons had to be pressed in the correct order. It turned out that Uncle Mort had given his relatives some pretty broad clues.

Sean: I remember he gave me one of those sudoku puzzles. He circled a bunch of numbers. They were all in a line on the middle row. I can't remember how many there were and I lost the paper.

Roseanne: Me too! And he said the numbers spelled a word in an "asking" code or something.

Chelsea: I forgot all about that until now. He did the same with me and then he wrote out the word. Then he told me: "now there's no way you can forget this" which just shows how dumb he is because I forgot it practically right away.

The others agreed that Uncle Mort had said the same thing to each of them. After a great deal of thought, Sean remembered that the word was three letters long and Roseanne remembered that it was written oddly: "Like, not all big or small letters?" And Chelsea remembered that it was either: "A capital letter, a small letter and a capital letter or small capital small."

If you were Chelsea's boyfriend, what combination would you suggest?

Answer

I would suggest the combination

73 45 61.

Firstly, the "asking" code combined with the row of numbers suggests that they spelled out a word in ASCII code. The numbers on the front of the safe only go to 100, so Mort was probably using the hexadecimal notation for ASCII, since the decimal notations for standard letters go up to 122.

The fact that all the numbers were on the same row in a Sudoku puzzle means that there were no repeated numbers and no zeroes. Combined with the restrictions on capital and small letters, this narrows the possible letters substantially, but ultimately there are still several possible words that could be made.

The actual key is that Mort said to all three children that "there's no way you can forget this." This indicates that there's some connection between the word and each child. As it happens, there's a three-letter word that they share right in their names - "sea".

The capitalisation rules mean that the original word could have been "SeA" or "sEa". Converting both to ASCII, the first becomes "53 65 41", which has two 5s and is therefore impossible due to the Sudoku. "sEa" becomes "73 45 61", and that is the most likely combination for the safe.