There are seven thieves, They steal diamonds from a diamond merchant and run away in jungle. While running, night sets in and they decide to rest in the jungle When everybody’s sleeping, two of the best friends get up and decide to distribute the diamonds among themselves and run away. So they start distributing but find that one diamond was extra. So they decide to wake up 3rd one and divide the diamonds again …..only to their surprise they still find one diamond extra. So they decide to wake up fourth one. Again one diamond is spare. 5th woken up……still one extra. 6th still one extra. Now they wake up 7th and diamonds are distributed equally.

** How many minimum diamonds they steal?**

Check your answer:-

See Solutionand

x = 1 + N1*2;

x = 1 + N2*3;

x = 1 + N3*4;

x = 1 + N4*5;

x = 1 + N5*6;

x = N6*7;

where N1, N2, N3, N4 and N5 are integers.

From above we can also say

N1*2 = N2*3 = N3*4= N4*5 = N5*6 = y

Now y should be divisible by 2, 3, 4, 5 and 6, its nothing but common multiple of all.

LCM of 2, 3, 2*2, 5, 2*3 => 2*3*2*5 => 60

at the same time common multiple + 1 should be divisible by 7 as well.

60 + 1 is not divisible by 7

120(60*2) + 1 is not divisible by 7

180(60*3) + 1 is not divisible by 7

240(60*4) + 1 is not divisible by 7

300(60*5) + 1 is divisible by 7

**Thus they must have stolen minimum 301 diamonds.**

Prashanth vunnam says

I found formula for this

x=3

43, x43, x043, x0043,x00043………xn43

those all possible cases we will get

Explanation

7*43=301 , 7*343=2401 and 7*3043=21301 …….so on all numbers give the answer

Aneesh Satheesan says

ANS: 301

150 * 2 +1=301

100 * 3 +1=301

75 * 4 + 1=301

60 * 5 + 1=301

50 * 6 + 1=301

43 * 7 =301

nibin says

91,721.. these are also correct

Gaurav k says

@nibin 91 cannot be divided equally into 4 + 1

91/4 = 22 + ‘3’ so when 91 is divided among 4 people sintead of 1, 3 are getting left

Anne J says

60x + 1 = 7y

7y must end with 1. (since 7y-1 should be divisible by 5 and 2 at the same time; i.e, 7y-1 should

be divisible by 10, or 7y must end with 1 )

hence y should end with 3 (no other digit can make 7y end with 3)

7y should be greater than 61

Trial and Error:

7(3)<61

7(13)= 91; 90 not divisible by 60

7(23)=161; 160 not divisible by 60

7(33)=231; 230 not divisible by 60

7(43)=301; 300 divisible by 60

@viccky says

but it can be 2401……???

Gaurav k says

How many ‘minimum’ diamonds they steal? we need to find out the minimum in this question