Puzzle of the Day : 59
There are 511 oranges and 9 empty boxes. An orange vendor asks his son to place all the 511 oranges in all the 9 boxes in such a manner that if he asks for any number of oranges from 1 to 511, his son should be able to pick them in terms of boxes. How did the son place all the oranges among the 9 boxes, given that any number of oranges can be put in one box? 1, 2, 4, 8, 16, 32, 64, 128, 256
The orange vendor can ask for only 1 orange, so one box must contain 1 orange.
He can ask for 2 oranges, so one box must contain 2 oranges.
He can ask for 3 oranges, in that case box one and box two will add up to 3.
He can ask for 4 oranges, so one box i.e. third box must contain 4 oranges.
Now using box number one, two and three containing 1, 2 and 4 oranges respectively, his son can give upto 7 oranges.Hence, forth box must contain 8 oranges.
Similarly, using first four boxes containing 1, 2, 4 and 8 oranges, his son can give upto 15 oranges. Hence fifth box must contain 16 oranges.
You must have noticed one thing till now that each box till now contains power of 2 oranges. Hence the answer is 1,2, 4, 8, 16, 32, 64, 128, 256. This is true for any number of oranges, here in our case only upto 511.
See our previous ‘Puzzles of the Day’:
https://tathagat.mba/puzzle-of-the-day-58/
https://tathagat.mba/puzzle-of-the-day-57/
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