Many years ago, a cruise liner sank in the middle of the Atlantic Ocean. The castaways luckily landed on a remote desert island.
There was enough food for the 135 people to last four weeks.
Nine days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 36 people stranded on the island to now share the original rationed food.
The food obviously had to be re-rationed, everyone was now on three-quarters of the original ration, so how many days in total would the food last, from the day of the original sinking?
Originally there was enough food for 135 people for 28 days, which totals 3780 rations.
After 9 days, 1215 rations had been eaten.
Therefore there were now 2565 rations left for 171 people, which would last for another 20 days at three-quarter rations per person = (2565 ÷ 3/4) ÷ 171.
Which is 29 days in total from the original sinking.
Hint
Start by filling the 9 gallon container, and then use that to fill the 4 gallon container.
Answer
Here are the contents of the containers after each stage:
A B
9 0 fill A
5 4 fill B from A
5 0 empty B
1 4 fill B from A
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A
6 0 empty B
This leaves 6 gallons in container A.
??
Puzzle 4
As my autumnal birthday approaches I like to collect leaves! A little bizarre perhaps, but I enjoy it!
Starting on the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on.
On my birthday, I will have collected 276 leaves altogether. Which day of the month is my birthday?
Bonus Question: how many days would it take for me to collect 56,616 leaves?