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Solution to: Weighing Marbles

Number the ten bags from 1 up to and including 10. Take the following number of marbles from each bag:

Bag numberNumber of marbles

In the numbers of marbles, you can recognize the famous Fibonacci sequence, in which every number after the first two is the sum of the two preceding ones: (0,) 1, 1, 2, 3, 5, 8, 13, ...

Place all 231 marbles that you took from the bags together on the balance. The number of grams that the total weight of these marbles is less than 2310 grams indicates the two bags with the marbles of 9 grams, according to the table shown below:

Bag numbers12345 6789
23 g--------
34 g5 g-------
46 g7 g8 g------
59 g10 g11 g13 g-----
614 g15 g16 g18 g21 g----
722 g23 g24 g26 g29 g34 g---
835 g36 g37 g39 g42 g47 g55 g--
956 g57 g58 g60 g63 g68 g76 g89 g-
1090 g91 g92 g94 g97 g102 g110 g123 g144 g

For example, if the weight of the marbles is 2268 grams, which is 42 grams less than 2310 grams, then bags 5 and 8 contain the marbles of 9 grams.

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