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Reasoning
Q1 can't have A as its answer (otherwise it would contradict itself).
If Q1's answer was C (meaning Q4's answer was A), then Q3's answer would be C. However, Q2's answer should now be A, but this isn't allowed by Q1 (as Q4 is the first answer with A). This is a contradiction.
Therefore, Q1's answer is B (meaning Q3's answer is A).
For Q2's answer to be C, Q4's answer would have to be A, which would contradict Q4. Therefore, Q2's answer is B making Q4's answer B.
If one small rabbit can dig a warren in nine hours, a medium rabbit can dig a warren in 6 hours, and a large rabbit can dig a warren in four and a half hours.
How long will it take one small, one medium, and one large rabbit, to dig a warren if they all work together?
Hint
How much of a warren can each rabbit dig in one hour?
Answer
2 hours.
Reasoning
The small rabbit can dig a warren in nine hours, so digs 1⁄9 in one hour.
The medium rabbit can dig a warren in 6 hours, so digs 1⁄6 in one hour.
The large rabbit can dig a warren in four and a half hours, so digs 1⁄4.5 in one hour.
1 Hour = 1⁄9 + 1⁄6 + 1⁄4.5
To make the denominators all the same, we can multiply through by 18⁄18 to give:
1 Hour = 2⁄18 + 3⁄18 + 4⁄18
1 Hour = 9⁄18
1 Hour = 1⁄2
So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.
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Puzzle 20
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.