With a 7-minute hourglass and an 11-minute hourglass, how would you time the boiling of an egg for 15 minutes?

There are actually two different ways: one takes more time but fewer moves than the other. Can you find them both?

Solution

Deep in a tropical jungle, the local chief is suspected of having a rare disease that is highly infectious. Three surgeons must operate on him, one at a time. To complicate matters, any one of the three doctors could have caught the disease while examining the chief. Each surgeon must wear rubber gloves when he operates. If he has the disease, its germs will infect the inside of any glove that touches his hand. And if the chief has the disease, it will contaminate the outside of any glove worn. However, there were only two pairs of sterile gloves available.

Can the surgeons operate without running the risk of catching the disease from the chief or from each other?

Solution

A shop was burgled but the loot was recovered. Three suspects were arrested: Adam, Basil and Colm. At the trial, they made the following statements:

Adam: I didn’t commit the robbery!

Basil:  Colm certainly didn’t!

Colm:  Yes, I did!

Later on, two of them confessed to having lied.

Who committed the robbery?

Solution

Mark was an extremely clever person who once asked his friend Bob the ages in years of his three children. The following conversation ensued:

Bob: The product of their ages is thirty-six.

Mark: That doesn't tell me their ages.

Bob: Well, by coincidence, the sum of their ages is your own age.

After several minutes of thought

Mark: I still don't have enough information.

Bob: Well, if this will help, my son is more than a year older than both his sisters.

Mark: Oh good! Now I know their ages.

What are their ages?

Solution

Suppose two trains are on the same railroad track 100km apart and heading towards each other, each at a speed of 50km/hr. A fly, initially on the front of one train, flies at 75km/hr towards the other oncoming train. On reaching it, the fly turns around (instantaneously) and flies back towards the first train. When it reaches the front of this train it turns around (again instantaneously) and flies back in the other direction.

How many kilometres will the fly have travelled in this hectic zigzag manner before it meets its inevitable fate?

Solution

Solution to Boiling an Egg:

One solution is to put the egg in boiling water and start both timers/hourglasses. When the 7-minute hourglass has run through, turn it over. When the 11-minute hourglass finishes running through, 4 minutes of the 7-minute hourglass will have run through (for the second time). Turning the 7-minute hourglass now and waiting until it runs through will have the egg boiling for a total of 15 minutes.

Can you find another solution which takes longer but involves fewer 'moves'?

Solution to Jungle Surgery:

The first surgeon wears both pairs of gloves, with pair A inside pair B. The second surgeon wears pair B. The third surgeon turns pair A inside out before wearing them.  

Solution to Liars:

Basil and Colm contradict one another, so one must be telling the truth and the other lying. Therefore, Adam is also lying and it was he who committed the robbery.

Solution to What are their Ages? :

The daughters are both 2-years-old and the son is 9. Although, there are several sets of three integers that can be multiplied to give 36, the numbers from only two of those sets have the same sum, 13 (i.e. 9+2+2=13 and 1+6+6=13). This is what prompts Mark to say that he still doesn’t have enough information. 

Solution to Zigzag:

It takes one hour for the two trains to meet in which time the fly covers 75km! Alternatively, the answer could be found as the sum of a series...