Marbles in bottle puzzle
You have 10 identical bottles of identical marble. Each bottle contain hundred of marbles. Out of 10 bottles 09 have 1 gram of marbles but 01 bottle has marbles of weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.
A modified version of the ‘Chocolate box’ puzzle (https://puzzlefry.com/puzzles/electronic-weighing-machine-to-fine-defective-chocolate-box-puzzle/)
Refer to the answer given to that puzzle. The same logic can be applied here. Number the bottles 1 to 10 and take as many marbles from each bottle as the bottle’s number and weigh. Since the ‘standard’ marbles are 1 g each, the total weight of the marbles, if all were standard, should be 55 g. (1 + 2 + 3 + … 10) The actual weight X obtained will be more than this (Because at least one marble selected weighs 1.1 g.) The difference (X – 55) divided by 0.1 will give the number of the bottle that contains the heavier marbles. e.g. if the weight obtained is 55.4 g, the bottle No. 4 contains heavier marbles (from which we had taken 4 marbles of 1.1 g each, resulting in 0.4 g excess weight.)
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