## Posts

### So – who stole the apple?

During lunch, 5 of Mr. Bryant’s students visit the supermarket.

One of the 5, stole an apple.

When questioned…

Jim said: it was Hank or Tom.
Hank said: neither Eddie or I did it.
Tom Said: you’re both lying
Don said: no one of them is lying, the other is speaking the truth.
Eddie said: no Don, that’s not true.

When the shop owner asked Mr. Bryant, he said that three of the boys are always truthful, but two lie all the time.

So – who stole the apple?

And the name of the person who stole the apple is......!

### Tom is an Apple Thief!

What's the story behind the title?

Let's recall who said what.

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Jim said: it was Hank or Tom.
Hank said: neither Eddie or I did it.
Tom Said: you’re both lying
Don said: no one of them is lying, the other is speaking the truth.
Eddie said: no Don, that’s not true.

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Clearly, Don and Eddie are making contradicting statements. Hence, one of them must be liar.

So there must be 1 more liar among Jim, Hank and Tom (since there are 2 liars & 3 truth tellers).

Tom's statement - you're both lying points Jim and Hank as liars. But there are total 2 liars with one being from either or Eddie as deduced above.

Hence, Tom himself must be that other liar.

Now we are sure that Jim and Hank must be telling the truth & as told by Hank, Eddie or Hank himself is not thief.

Since, Hank is not the one who stole the app…

### Divide 1 Cube into 20 Cubes!

From a 1987 Hungarian math contest for 11-year-olds:

How can a 3 × 3 × 3 cube be divided into 20 cubes (not necessarily the same size)?

Cut this way to get 20 cubes....

### Division of 1 Cube into 20 cubes

What was the challenge?

Mark cube for cutting 3 x 3 x 3 = 27 cubes. Cut any section of 2x2x2 = 8 cubes & cut rest of 27-8 = 19 cubes. So these 19 cubes plus 1 cube of 2x2x2 give us total number of 20 cubes.

### Need of Speed For Average Speed

A man drives 1 mile to the top of a hill at 15 mph. How fast must he drive 1 mile down the other side to average 30 mph for the 2-mile trip?

Here is calculation of that speed needed!

### Impossible Average Speed Challenge

What was average speed challenge?

A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e.4 minutes to reach at the top of a hill.

To achieve average speed of 30 mph, the man has to complete 2 miles trip in 1/15 hours i.e. 4 minutes. But he has already taken 4 minutes to reach at the top of a hill, hence he can't achieve average speed of 30 mph over entire trip.

MATHEMATICAL PROOF:

Let 'x' be the speed needed in the journey down the hill.

Average Speed = Total Distance/Total time

Average Speed = (1 + 1)/(1/15 + 1/x)

30 = 2/(1/15 + 1/x)

### A Visit To Grandmother's Home!

A father wants to take his two sons to visit their grandmother, who lives 33 kilometers away. His motorcycle will cover 25 kilometers per hour if he rides alone, but the speed drops to 20 kph if he carries one passenger, and he cannot carry two. Each brother walks at 5 kph

Can the three of them reach grandmother’s house in 3 hours?