Math, asked by akr2929, 1 year ago

there are seven thieves,they steal diamond from a diamond merchant and run away in Jungle.While running night sets in and they decide to rest in jungle.When every body is sleeping,two of them the best friends get up and decide to distribute the diamonds among themselves and run away.So they started distributing but found that one diamond was extra.So they decide to wake up third one and divide the diamond again. Only to their surprice they still find one diamond extra.So they decide to wake up 4th one ,again one diamond is spare.%th woken up ,still one extra.6th still one extra.Now they wakeup seventh and diamonds are distributed equally.How many diamonds in total they steal

Answers

Answered by poojan

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

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