A lottery is organized as follows. Tickets that bear the numbers 1 , 2 , 3 , . .

Question

A lottery is organized as follows. Tickets that bear the numbers 1, 2, 3, . . . , 2013 are placed into a box (there are exactly 2013 tickets). The lottery director repeatedly removes a handful of tickets, adds the numbers that are shown and calculates the remainder that is left when this sum is divided by 17. A new ticket showing this remainder is placed back into the box before the director removes another handful of tickets. On one occasion, the director continued this process until exactly two tickets were left in the box (after the last remainder had been returned). If one of these tickets showed the number 2000 what did the other show?

Explanation / Answer

ans = 0

because reminder =remainder when summation( ( 1+ 2 +3....+2013) - 2000 ) is divided by 17

= 0

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