How many were in the pile the previous evening

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Reference no: EM133345517

Case: As every year Santa and his 99 elves have been busy making loads of presents for all the children in the world. The night before Christmas they put all the presents in a big pile in the workshop. Santa told the elves that the next morning they would evenly distribute the presents among the 99 elves for delivery to the children. All the elves were happy with the work they had done, full of anticipation for the next day, and also tired. So they went off to their bedrooms.

In the middle of the night one of the elves woke up. Excited and unable to fall asleep again he decided to get started early on the days work. He went out to the workshop and separated the presents into 99 equal piles. One extra present was left, so he put that one extra present and one pile of presents into his sack and pushed the other 98 piles back together.

Then he went off on his work without waking Santa or any of the other elves. Just a little time later another elf awoke and decided to start early. Unaware that some presents had already been taken from the pile in the workshop he took one 99th of the presents and again exactly one extra present that was left after dividing into 99 and he left the other presents behind in one big pile.

Before morning came all the other elves also woke up early and one after another repeated the same procedure, each time with the same result of taking one of 99 piles and exactly one extra present that was left after the division.

Finally Santa gets up as the sun rises. Much to his surprise he finds no elves and only a minimum number of present in the workshop. How many presents were left in the morning and how many were in the pile the previous evening?

Reference no: EM133345517

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