Question 26
An elf lives in the fairy world. One day he chooses 12 pairs of positive numbers: the first pair consists of odd numbers, the second of numbers leaving remainder 1 on division by 3, the third of numbers leaving remainder 1 on division by 4, and so on through the twelfth pair. He calculates the difference of the squares in each pair and writes the product of all the differences on a blackboard.
Starting the next morning, he divides the number on the board by 12. If the result is an integer, he replaces the number by that result; otherwise he erases everything and moves to the human world to play pranks. For how many days, excluding the initial day when he chooses the numbers, are we guaranteed to have no trouble in our world?
(A) 4 (B) 5 (C) 6 (D) 8 (E) 12.
Starting the next morning, he divides the number on the board by 12. If the result is an integer, he replaces the number by that result; otherwise he erases everything and moves to the human world to play pranks. For how many days, excluding the initial day when he chooses the numbers, are we guaranteed to have no trouble in our world?
(A) 4 (B) 5 (C) 6 (D) 8 (E) 12.