Diamond stealing puzzle
There were certain diamonds in a shop.
- thief stole half of diamonds and 2 more.
- thief stole half of remaining and 2 more
- same as above
- same as above.
- came nothing was left for that.
how many diamonds were there???
Why the author said “same as above”?
Because: The steps were:
1.thief stole half of diamonds and 2 more.
2.thief stole half of diamonds and 2 more.
3.Same as above(It means here 1,2 steps repeated again. So the thief stole twice more)!
4.Same as above(It means now more four steps repeated)
As a result the thief actually stole 8 times.
At last there was no diamond left.
So 8th time when the thief stole 2 diamonds there were only two diamonds left!
Now we can guess there were 1,2,3,4,5,6,…….diamonds when the thief stole for the second time!!
But actually there were only 4.
Because the thief stole half of the 4 diamonds=2 and remaining two. And this way he stole 4 diamonds!!
As a result for the nineth time he got nothing.
No other number will satisfy this clue!!
So when the thief stole for the 8th time there were 4 diamonds!!
For 7th time he stole half of the remaining and 2 more.
So there were (4+2)*2=12 diamonds!!
For 6th time he stole half of the remaining and 2 more.
So there were (12+2)*2=28 diamonds!!
For 5th time he stole half of the remaining and 2 more.
So there were (28+2)*2=60 diamonds!!
For 4th time he stole half of the remaining and 2 more.
So there were (60+2)*2=124 diamonds!!
For 3rd time he stole half of the remaining and 2 more.
So there were (124+2)*2=252 diamonds!!
For 2nd time he stole half of the remaining and 2 more.
So there were (252+2)*2=508 diamonds!!
For 1st time he stole half of the remaining and 2 more.
So there were (508+2)*2=1020 diamonds!!
If my initial logic was wrong there were only 4 steps!!
And the answer became 60.
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