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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 , 5 Years ago
Grade 6
anser 1 Answers
Aditya Gupta

Last Activity: 5 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.
KINDLY APPROVE :))
 
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