The Mangoes Problem


One night the King couldn't sleep, so he went down into the royal kitchen where he found a basket full of mangoes. He was hungry, so he ate 1/6 of the mangoes.

Later that night, the Queen was hungry and she couldn't sleep. She went down to royal kitchen and she found the basket of mangoes, and she ate 1/5 of what was left.

Still later, the Prince awoke, went down to the kitchen, and ate 1/4 of the mangoes that were left.

Even later, his sister, the Princess, woke up and went down to the kitchen. She found the basket of mangoes, and ate 1/3 of the mangoes she found.

Finally, the royal dog came by and found the mangoes. He ate 1/2 of the mangoes he found.

The next morning the cook came down to make breakfast for the royal family. She found only 3 mangoes left in the basket.


How many mangoes were originally in the basket the night before?