Answer :
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.
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