Two young math students are trying to develop a new notation for numbers for a class project. They want it to be based on completely different principles from decimal notation. Joe decides to try using a "word" of X's and O's, where the first letter tells you if the number is divisible by 2, the second letter indicates if it's divisible by 3, then 4, and so forth. An X means yes, and an O means no.
Here is how the first few numbers would be represented in Jonah's system: 1=O, 2=X, 3=OX, 4=XOX, 5=OOOX, 6=XX.
Jonah tells Alice that he has chosen a number between 1 and N, inclusive, and that he has represented it by a 9-letter word (indicating divisibility by 2 through 10). Alice, sitting across the table, looks at the word and says that the number must be A. Jonah is puzzled because that is not the number he chose. Alice, seeing his confusion, quickly realizes what the problem is, and gives him the expected answer.
What were Jonah's and Alice's numbers?
(In reply to
re(2): question by Jer)
That makes much more sense!
Unfortunately, I didn't find any pairs of 9-letter words where one is the reverse of another. So perhaps my interpretation of the notation is incorrect, or my program for finding notations is flawed, or something else.
For whatever it's worth here are the 9-letter words I found:
50 xooxoooox
80 xoxxooxox
100 xoxxoooox
150 xxoxxooox
300 xxxxxooox
350 xooxoxoox
450 xxoxxooxx
480 xxxxxoxox
540 xxxxxooxx
560 xoxxoxxox
700 xoxxoxoox
720 xxxxxoxxx
1050 xxoxxxoox
1680 xxxxxxxox
1890 xxoxxxoxx
2100 xxxxxxoox
3780 xxxxxxoxx
5040 xxxxxxxxx
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Posted by tomarken
on 2024-02-19 08:28:17 |
re(3): question
