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Seven thieves and diamonds

(14 votes, average: 3.79 out of 5)

January 12, 2014 by puzzler 7 Comments

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:-

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See SolutionHide Solution
Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
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.

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Comments

  1. Prashanth vunnam says

    July 21, 2017 at 10:05 pm

    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

    Reply
  2. Aneesh Satheesan says

    December 5, 2015 at 11:06 pm

    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

    Reply
  3. nibin says

    June 26, 2014 at 6:39 am

    91,721.. these are also correct

    Reply
    • Gaurav k says

      May 18, 2015 at 2:40 pm

      @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

      Reply
  4. Anne J says

    January 21, 2014 at 3:36 am

    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

    Reply
    • @viccky says

      June 11, 2014 at 6:55 pm

      but it can be 2401……???

      Reply
      • Gaurav k says

        May 18, 2015 at 2:41 pm

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

        Reply

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