Second semester officially open

For the first day of the second semester, I have decided to go easy on the dormant minds of the students. I bet they're more sleepy than dormant, since I can see an unexpected vivacity in their eyes. We start off by a reflection on the previous term. What did they enjoy? What would they like to see improved? What was difficult?

I don't know about you but I always thought that there's nothing like a good problem to hook you up to the matter. I selected this one for my grade seven monsters:

One night, Mint, Nett, Kate, Rakjang and Mai were having a sleep over at Mint’s place.

Mint couldn’t sleep so she went down to the kitchen, where she found a bowl full of mangoes. She ate 1/6 of the mangoes and went back to sleep.

Later that same night, Nett was hungry so she took 1/5 of the remaining mangoes.

Still later, Kate awoke, went down to the kitchen and ate 1/4 of the mangoes Nett had left.

Even later, Rakjang ate 1/3 of what was then left.

In the morning, Mai ate 1/2 of the remaining mangoes for breakfast, leaving only 3 mangoes for the dog.

How many mangoes were originally in the bowl?

And a little bit more challenging:

Three sailors were marooned on a deserted island that was also inhabited by a band of monkeys. The sailors worked all day to collect coconuts but they were too tired to count them so they agreed to divide them equally the next morning.

During the night, one sailor woke up and decided to get his share. He found that he could make three equal piles, with one coconut left over, which he threw to the monkeys. Thereupon, he had his own share and left the remainder in a single pile.

Later that night, the second sailor awoke and, likewise, decided to get his share of the coconuts. He also was able to make three equal piles, with one coconut left over, which he threw to the monkeys.

Somewhat later, the third sailor awoke and did exactly the same thing with the remaining coconuts.

In the morning, all three sailors noticed that the pile was considerably smaller but each thought that he knew why and said nothing. When they then divided the remaining coconuts equally, each sailor received seven and one was left over, which they threw to the monkeys.

How many coconuts were in the original pile?

I expect good cooperation work in this class, that may result in a variety of approaches.