Unique Audiance For A Fairy Tale

A sultan has 14 daughters. He decides to tell every night four of his daughters a fairy tale, but in such a way that every night, there will be another combination of four daughters. How many nights will keep the sultan busy telling fairy tales? 

Find number of nights here!

Nights For Fairy Tales!

Story behind the title?

For a moment, let's name all the daughters as A, B, C, D, E.....N. 

There are 14 x 13 x 12 x 11 = 24024 combinations of daughters. But in these combinations, lots of combinations are repeated. For example, ABCD combination is same as ABDC or DABC etc. There can be 4 x 3 x 2 x 1 = 24 combinations while considering group of 4 daughters here for example it is A, B, C, D. For these 24 combination we should count only 1 as a unique combination.

Hence for 24024 combinations, we have 24024/24 = 1001 unique combination. 

In short, Sultan would be busy for 1001 nights in telling fairy tales to his 14 daughters in unique combinations.

Numbers For The Letters?

A - B = B

B * C = A

D : B = E

C * C = E

C + E = A

For which numbers stand A, B, C, D and E? 

Skip To The Answer!  

Correct Numbers For Letters

What was the question? 

Let's first rewrite all equations and number them

1. A - B = B

2. B * C = A

3. D : B = E

4. C * C = E

5. C + E = A

For which numbers stand A, B, C, D and E? 

From 1, A = 2B. Putting this in 2 gives,

C = 2.

Putting C = 2 in 4 gives, E = 4.

So from 5, A = C + E = 2 + 4 = 6.

Equation 2 gives, B = A/C = 6/2 = 3.

And equation 3 gives D = B * E = 3 * 4 = 12.

Conclusion : A = 6, B = 3, C = 2, D = 12 and E = 4.