Marble
Factory Challenge
Answer:
The contents or the ten bags (in marbles) are as follows:
1 2 4 8 16 32
64
128 256 489.
PS: The participant was asked to find 94 marbles.
AI answer
This is a
classic problem that involves distributing a set of items (in this
case, marbles) into containers (bags) with the goal of creating a
specific distribution that allows for easy retrieval.
In this scenario, you want to distribute 1000 marbles among 10 bags in
such a way that someone can ask for any number of marbles up to 1000,
and you can give them the requested amount by handing over one or more
bags without counting the marbles.
One way to achieve this is to use binary representation.
Distribute the marbles in the following pattern:
- Bag 1: 1 marble
- Bag 2: 2 marbles
- Bag 3: 4 marbles
- Bag 4: 8 marbles
- Bag 5: 16 marbles
- Bag 6: 32 marbles
- Bag 7: 64 marbles
- Bag 8: 128 marbles
- Bag 9: 256 marbles
- Bag 10: 489 marbles
The key here is that each bag contains a specific power of 2 number of marbles.
When someone asks for a certain number of marbles, you can give them a combination of bags that adds up to that number.
Since any number up to 1000 can be represented as a sum of powers of 2,
this distribution allows for easy retrieval without counting.
For example:
- If someone asks for 7 marbles, you can give them
Bag 1 (1) + Bag 2 (2) + Bag 4 (4).
- If someone asks for 143 marbles, you can give them
Bag 1 (1) + Bag 2 (2) + Bag 8 (128) + Bag 16 (16) - a total of 147 marbles.
This way, the participant can request any number of marbles up to 1000,
and you can give them the exact amount without counting the marbles.
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