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 is 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 diamond again....
Only to their surprise, they still find one diamond extra.
So they decide to wake up the fourth one. And 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..

So, How many minimum number of diamonds did they steal??

sneha singh, 10 years ago

Grade:12

8 Answers

Sunil Kumar FP

askIITians Faculty 183 Points

10 years ago

minimum no of diamond is 721.

soln-1×2×3×4×5×6 +1=721

remainder shouls be 1 in each case of divisibility.

thanks and regards

sunil kr

askIItian faculty

Pushkar Aditya

71 Points

10 years ago

yes he is correct, answer is 301

SADDAM NAFEES

26 Points

10 years ago

Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
x = 1 + R1*2;
x = 1 + R2*3;
x = 1 + R3*4;
x = 1 + R4*5;
x = 1 + R5*6;
x = R6*7;
where R1, R2, R3, R4 and R5 are integers.
From above we can also say
R1*2 = R2*3 = R3*4= R4*5 = R5*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

Thanks & Regards

SADDAM NAFEES

askIITians Faculty

prudhvi G

12 Points

10 years ago

301 is the answer and there are many solutions possible.among them least value is 301.in general the no.(60k+1) if divisible by 7 then all r the solutions

Ramesh

8 Points

10 years ago

answer is 301... minimum number of diamonds are {integer multiple of (LCM(2,3,4,5,6) )+1} so we have to select the integer in such a way that the number is exactly multiple of 7. So the answer is 301.

Prashanth Vunnam

11 Points

6 years ago

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

Gsrinivas

13 Points

6 years ago

We need remainder 1 when divided by 2,3,4,5,6. So find LCM of them. We get 60. Now 60+1=61 but 61 is not divisible by 7. So have go by trial and error method only. Multiple of 60 +1 should be divisible by 7.So 61, 121,181,241,301.... Among these 301 is divisible by 7So least required number is 301..Now LCM of 2,3,4,5,6 and 7 is 420301 + 420 = 721 (property of factors)721 + 420 =11411141 + 420 = 1561...

Vallinayagam

13 Points

5 years ago

We need the no which is not divided by 2 ,3,4,5,6 and it should be divided by 7

So ,first we can try with square no of 7

=49

2×25 =50 so,it cannot be divided

3×16=48 so,it cannot be divided

4×12=48 so,it cannot be divided

5 ×10=50 so,it cannot be divided

6×7=48 so,it cannot be divided

But it is divided by 7 because it is a square no of 7 so the minimum no of diamond they steal are 49