# Rich man’s and gold Coin puzzle

A rich man died. In his will, he has divided his gold coins among his 5 sons, 5 daughters and a manager.

According to his will: First give one coin to manager. 1/5th of the remaining to the elder son. Now give one coin to the manager and 1/5th of the remaining to second son and so on….. After giving coins to 5th son, divided the remaining coins among five daughters equally.

All should get full coins. Find the minimum number of coins he has?

This is an interesting problem.

We know that if the fifth son gets x5 then the fourth son gets x4 = 5*(x5 + 1)/4 – 1 = x5 + (x5+1)/4 and third son gets x3 = 5*(x4 + 1)/4 – 1 = x4 + (x4+1)/4 and so on. Representing what each son gets in terms of what the fifth son gets gives:

x3 = x5 + (x5+1)/4 + ((x5+(x5+1)/4))/4

= x5 + (x5+1)/4 + 5(x5+1)/16

x2 = x5 + (x5+1)/4 + 5(x5+1)/16 + 25(x5+1)/64

x1 = x5 + (x5+1)/4 + 5(x5+1)/16 + 25(x5+1)/64 + 125(x5+1)/256

From this we know that the fifth son (x5) must get a number of coins that can be expressed in the form x5 = 256y – 1.

The other requirement is that x5 must be a multiple of 5, because each daughter gets 4/5 of what the 5th son gets. That means that the final digit of y must be either 1 or 6 so that the final digit of 256y is 6. The smallest such value for y is 1, making x5 = 255.

Plugging in 255 for x5 gives

x1 = 624

x2 = 499

x3 = 399

x4 = 319

x5 = 255

with each daughter getting 4/5 * 255 = 204 and the manager getting 5 gold coins

204 * 5 + 255 + 319 + 399 + 499 + 624 + 5 = 3121 = 624 * 5 + 1. The minimum number of coins is 3121.

The second smallest number of coins possible is 18,746, which results from setting y = 6.

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »### What is the age of grand father puzzle

A boy asks his father, “what is the age of grand father?“. Father replied “He is x years old in ...Read More »### Maths Genious Riddle

If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »