A sheikh has to transport 100 gold bars of 1 kilo of weight each. For this it has 10 camels and 1 guard for each camel. Each of these camels carries 10 ingots.
At the end of the trip, the sheikh's confidant tells him that one of the guards has stolen 1 gram of gold from each of the 10 bullion that the guard was carrying but does not know with certainty what guard he is. How can the sheikh guess which guard has robbed him, knowing that he only has one scale with which he can perform a single weighing?
Note: We have a scale and not a scale. That is, it measures the exact weight of what is placed on it.
One possible way would be the following: You take an ingot of the first camel, two ingots of the second, three of the third and so on until the last camel. They are all weighed together on the scale and if 1 gram is missing, we know with certainty that the thief is the guard of the first camel (since we only put one of his ingots), if 2 grams are missing the thief is the guardian of the second camel, if missing 3 is the guardian of the third camel and so on.