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Grade 6Algebra

Five thieves broke into the jeweler's shop and stole only diamonds.

Thief 1 took one half of the first diamond and a diamond
Thief 2 took one-half of the rest of the diamond and a diamond.
Thie f3 took one-half of the rest of the diamond and a diamond.
Thief 4 took one-half of the rest of the diamond and a diamond.
Thief 5 didn't have any diamonds left to take.

Question: So how many diamonds were there in the jewelry store at first?

RI FIEK

6 Years agoGrade 6

1 Answer

Aditya Gupta

6 Years ago

the lang of ur ques is a bit unclear. however i ll try my best to ans it.

let the no. of inital diamonds be A_0.

after thief 1 commits his crime, let the no of diamonds LEFT be A_1.

similarly after thief 2 commits his crime, let the no of diamonds LEFT be A_2 and so on.....

clearly, A_(n+1) = A_n – (A_n/2 + 1)

or 2[1 + A_(n+1)] = A_n

also, A_4= 0

So, A_3= 2(1+0)= 2

so A_2= 2(1+2)= 6

so A_1= 2(1+6)= 14

or A_0= 2(1+14)= 30

Hence there were 30 diamonds initially.

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