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A warehouse has 10 unlabelled rows of pallets. Each row of pallets contains thousands of cell phones destined for different countries. Each 100 gram cell phone is exactly the same except for those in the row destined for Japan, which have a “special” 2 gram chip encased within each phone to make sure it works on the Japanese networks.

How can the warehouse manager make sure the right phones go to Japan in the quickest time possible? All the warehouse manager has at his disposal is a digital balance.

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migrated from Nov 21 '11 at 13:59

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If this is homework, please tag it as 'homework'. Regardless, please share with us what you have attempted so far. What is the maximum capacity of the digital scale? We don't want to break the manager's only scale, do we? – jthetzel Nov 21 '11 at 1:29
How does statistics enter into this problem? It seems to be similar to one of several math puzzles involving minimum number of steps to identify the odd piece. If so, this question may be off-topic here and perhaps on topic on math.SE. – varty Nov 21 '11 at 4:57
Do the phones intended for Japan weigh $102$ grams instead of $100$ grams? I don't get this from the problem statement, e.g. the $2$ gram chip in phones intended for the Japanese market might be replacing a $1.5$ gram chip, which would make @PeterFlom's solution not work.... Please edit your problem statement to state the weight of the special phones explicitly. – Dilip Sarwate Nov 21 '11 at 15:55

This is an old old puzzle that can be found in many books.

Solution: Weigh 1 cell phone from row 1, 2 from row 2 and so on, all at the same time. Divide the weight by 100. Divide the remainder by 2. That's the row number with the Japanese phones.

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You probably want to subtract $5500$, not divide by $100$. A total of $55$ phones are being weighed, and so the total weight is $5500 + 2n$ where the $n$ phones from pallet $n$ are contributing an extra $2n$ grams of weight. – Dilip Sarwate Nov 21 '11 at 19:53

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