One night the king couldn't sleep, so he went down into the royal kitchen, where he found a bowl full of mangoes. being hungry, he took 1/6 of the mangoes. later that same night, the queen was hungry and couldn't sleep. she, too, found the mangoes and took 1/5 of what the king had left. still later, the first prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. even later, his brother, the second prince, ate 1/3 of what was then left. finally, the third prince ate 1/2 of what was left, leaving only three mangoes for the servants. how many mangoes were originally in the bowl? is there more than one solution?

If you think in picture, it will be easier
1. king --1/6 of all
2. queen -- 1/5 of what king had left (remaining)
3. 1st prince -- 1/4 of remaining
4. 2nd prince -- 1/3 of remaining
5. 3 rd prince -- 1/2 of remaining
6. there are 3 mangoes left

so if we think that there are 6 parts of all
1. king took 1st part (5 parts left)
2. queen took 1 of what king had left which he left 5 parts (4 parts left)
3. 1st prince took 1 of 4 (3 parts left)
4. 2nd prince took 1 of 3 (2 parts left)
5. 3rd prince took 1 of 2 (1 part left)
that means 1 part equals 3 mangoes
so we have 6 parts at first then there were 18 mangoes originally in the bowl.

i think there is only 1 answer.