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. Therefore, they decide to wake up the 3rd one and divide the diamonds again. Only to their surprise they still find one diamond extra. Yet again, 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 diamonds in total they stole?
Answers
The total diamonds stolen by the thieves are 301 in number
Explanation:
There were seven thieves in all.
Suppose they stole x diamonds in total.
It says that if 7 of them distribute the diamonds among them equally, no diamond will be left. i.e., x is exactly divisible by 7.
If 2 thieves share the diamonds between them, one diamond will be left.
i.e, x = 1 + T 1 * 2 --------------- 1
If 3 thieves share the diamonds among them, one diamond will be left.
i.e., x = 1 + T 2 * 3 --------------- 2
If 4 thieves share the diamonds among them, one diamond will be left.
i.e., x = 1 + T 3 * 4 --------------- 3
If 5 thieves share the diamonds among them, one diamond will be left.
i.e., x = 1 + T 4 * 5 --------------- 4
If 6 thieves share the diamonds among them, one diamond will be left.
i.e., x = 1 + T 5 * 6 --------------- 5
If all 7 thieves distribute the diamonds among them, no diamond will be left. i.e, x = T 6 * 7 --------------- 6
If we see the first 5 equations, we can observe that in all the situations only 1 diamond left.
So, we can say that T1*2 = T2*3 = T3*4 = T4*5 = T5*6 = y
From this, we get to know that 2, 3, 4, 5, 6 are the common multiples of y.
The least common factor (LCM) here is : LCM(2,3,4,5,6) = 60
As we know that one diamond will be left,
The answer would be the common multiple + 1 and it should be divisible by 7.
60 + 1 = 61 => No, because it is not divisible by 7.
60*2 + 1 = 121 => Not divisible by 7.
60*3 + 1 = 181 => Not divisible by 7
60*4 + 1 = 241 => Not divisible by 7
60*5 + 1 = 301 -> DIVISIBLE!
So, the diamonds that are stolen by the 7 thieves are 301 in number.
Learn more:
Similar question.
https://brainly.in/question/642191
https://brainly.in/question/905