Seven students count from 1 to 1000 as follows:

1. Adela says all the numbers, except she skips the middle number in each consecutive group of three numbers. That is, Adela says 1, 3, 4, 6, 7, 9,..., 997, 999, 1000.
2. Becky says all of the numbers that Adela doesn't say, except she also skips the middle number in each consecutive group of three numbers.
3. Carina says all of the numbers that neither Adela nor Becky says, except she also skips the middle number in each consecutive group of three numbers.
4. Deidre says all of the numbers that none of Adela, Becky or Carina say, except she also skips the middle number in each consecutive group of three numbers.
5. Edith says all of the numbers that none of Adela, Becky, Carina or Deidre say, except she also skips the middle number in each consecutive group of three numbers.
6. Francine says all of the numbers that none of Adela, Becky, Carina, Deidre or Edith say, except she also skips the middle number in each consecutive group of three numbers.
7. Finally, Glen says the only number that no one else says.

What number does Glen say?

Adela skips all the numbers that are 2 mod 3.

Becky skips all the numbers that are 5 mod 9.  (5 = 2 + 3, 9 = 3^2)

Carina skips all the numbers that are 14 mod 27.  (14 = 5 + 9, 27 = 3^3)

Deidre skips all the numbers that are 41 mod 81.  (41 = 14 + 27, 81 = 3^4)

Edith skips all the numbers that are 122 mod 243.

Francine skips all the numbers that are 365 mod 729.

Therefore the only number that remains for Glen to say is 365.

 

 

Posted by tomarken on 2014-07-31 15:15:40