The Fearsome Logical Challenge

You and your two friends Pip and Blossom are captured by an evil gang of logicians. In order to gain your freedom, the gang’s chief, Kurt, sets you this fearsome challenge.

The three of you are put in adjacent cells. In each cell is a quantity of apples. Each of you can count the number of apples in your own cell, but not in anyone else’s. You are told that each cell has at least one apple, and at most nine apples, and no two cells have the same number of apples.

The rules of the challenge are as follows: 

The three of you will ask Kurt a single question each, which he will answer truthfully ‘Yes’ or ‘No’. Every one hears the questions and the answers. He will free you only if one of you tells him the total number of apples in all the cells.

    Pip: Is the total an even number?

    Kurt: No.

    Blossom: Is the total a prime number?

    Kurt: No

You have five apples in your cell. What question will you ask?

THIS should be the question that you need to ask!

Logical Response to The Fearsome Challenge

What was the challenge?

Remember, all you have to do is that ask one crucial question to logicians and not necessarily deduce the total count of apples.

Since, each cell has 1 to 9 apples and no two cells have same number of apples, the lowest count of apple is 1 + 2 + 3 = 6 and the highest count would be 7 + 8 + 9 = 24.

That is the total number of apples could be between 6 to 24.

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Now, Pip and Blossom already have gathered some information about the total.

1. The total is not an even number - Hence, only numbers  7,9,11,13,14,15,17,19,21,23 can represent the total count.

2. The Total is not a prime number - Out of the number above, only 9, 15, 21 are non-prime number.

Hence, the total count must be among 9,15 or 21.

Now, your task is easier. All you need to ask the Kert below question -

"Is total is 15?"
 
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CASE 1 : Total is really 15 -

Then Kert would reply with YES to your question and all of you know the total now.

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CASE 2 : Total is 9 -

The Kert's answer to your question would be NO.

If the total is 9 and you have 5 apples then rest of 4 apples must be distributed among Pip and blossom as (1,3) or (3,1) but can't be (2,2) since no 2 cells can have same number of apples.

Now, the friend having 1 apple (or 3 apples) can think that the total can't be 21 as in that case other 2 must have total of 20 (or 18) apples. But the maximum that other two can have is 9 + 8 = 17 apples.

So any of them can deduce that the total is 9.

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CASE 3 : Total is 21 -

Since you have 5 apple other 2 must be having total of 16 apples. One of them must be having 7 apples and other having 9 apples.

The friend having 9 apples can easily deduce the count as 21 since 9 as a total count is impossible in the case as for that the other must have 0 apples.

And the friend with 7 apples know that other can't have 1 + 1 or 2 + 0 (as per given data) apples in order to have total count of 9. Hence, he too can deduce that the total must be 21.

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To conclude, depending on the what Kert answers to your question and the count of apples that each of other 2 friends have one of them (or you too if count is 15) can deduce the total number of apples easily. And eventually, logicians have to set you free as promised.

The Apple Conundrum

Two women are selling apples. The first sells 30 apples at 2 for $1, earning $15. The second sells 30 apples at 3 for $1, earning $10. So between them they’ve sold 60 apples for $25.

The next day they set the same goal but work together. They sell 60 apples at 5 for $2, but they’re puzzled to find that they’ve made only $24.

What became of the other dollar?

Here, could be that lost dollar! 

Behind The Apple Conundrum

What is the conundrum?

They sell 60 apples at 5 for $2, that means 12 such sets of 5 apples. Suppose, out of each such set, 1 woman takes out $1 for 2 apples and other takes $1 for 3 apples. So, first woman earns $12 by selling 24 apples and second woman sells 36 apples for $12.

In short, first woman gives away 6 apples (from her 30 apples) to second woman increasing her count to 36 reducing her own count to 24. First woman would have made $3 from those but second woman only made $2 from those 6 apples. And there is that lost dollar in earning.

So, 60 apples can't be divided equally to find the earning as they had sold apples at different rates on previous day.

Other way, if they wanted to sell apples together with 30 apples each, then they should have sold apples at average of (1/2 + 1/3)/2  = $5/12 per apple (i.e. 12 apples for $5) instead of $2/5 per apple.

The difference in price per apple (5/12 - 2/5) = (1/60).

So the difference in earning after selling 60 such apples = (1/60) x 60 = 1.

And there is that other dollar! 

What's wrong gone here on next day? Instead of averaging dollars per apple, apples per dollar are added directly which resulted reduced cost of each apple. 

Mixed up Apples at the Farm

Someone has mixed up the apples. Read carefully what has happened. Can you find a way to help solve the problem.

• There are 10 baskets containing apples.

• There are various amounts of apples in each basket ranging from 10 to 20.

• 9 of the baskets contain apples weighing 4 ounces each.

• 1 of the baskets contains apples weighing 5 ounces each.

• All the apples look the same.

• The equipment you have is a set of scales and an empty basket.

• It is late and the truck is waiting to take the apples to market. You only have time to make one measurement using the scales. 

Take out the basket contains apples weighing 5 ounces each.

Here is how you can identify that basket! 

Source 
  

Sorting of Mixed Up Apples

How they were mixed?

Let's number all the baskets from 1 to 10. Just take out 1 apple from first basket, 2 from second, 3 from third & so on. We would have 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 apples now. If each of them was of 4 oz, then these 55 apples together would have weighed as 55 x 4 = 220 oz. Since 1 basket have apples each weighing 5 oz, these 55 apples would weigh more than 220 oz.

Let's say it weighs 222 oz, then the 2 apples taken by second basket must be of 5 oz each. And if it weighs 228 then there are 8 apples weighing more than 4 oz (i.e. 5 oz each). Hence that eight basket must have all apples weighing.

So depending on how much weight of 55 apples exceeds 220 oz, we can identify the basket with apples weighing 5 oz each.  

 

How Many Apples in a Basket?

In a guess game , five friends had to guess the exact numbers of apples in a covered basket.Friends guessed as 22 , 24, 29 , 33 , 38, but none of guess was right.The guesses were off by 1, 8, 6, 3, and 8 (in a random order).

From this information, can you determine the number of apples in a basket ?

Logic to get the answer! Click here! 

Source 

Number of Apples in a Basket

What was the game? 

There are 2 guesses which were off by 8. That means exact number must be guess (1) + 8 & guess (2) - 8. So those 2 guess must differ by 16 from each other. And there are 2 guesses in given list differing by 16 & those are 22 & 38. Hence the exact number of apples in a covered basket is 30. Let's verify with all guess & errors.

22 + 8 = 30

24 + 6 = 30

29 + 1 = 30

33 - 3 = 30

38 - 8 = 30