MODBasic LogicalAndReasoning AMC10/12 Difficult
2011


Problem - 1457

Seven students count from $1$ to $1000$ as follows:

  • Alice says all the numbers, except she skips the middle number in each consecutive group of three numbers. That is, Alice says $1$, $3$, $4$, $6$, $7$, $9$, . . ., $997$, $999$, $1000$.
  • Barbara says all of the numbers that Alice doesn't say, except she also skips the middle number in each consecutive group of three numbers.
  • Candice says all of the numbers that neither Alice nor Barbara says, except she also skips the middle number in each consecutive group of three numbers.
  • Debbie, Eliza, and Fatima say all of the numbers that none of the students with the first names beginning before theirs in the alphabet say, except each also skips the middle number in each of her consecutive groups of three numbers.
  • Finally, George says the only number that no one else says.

What number does George say?


The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for $99.

report an error