What's the minimum number of boxes you need to open before you know what is contained in all the boxes?

Found this problem: And the correct answer is: 2

Counter-Argument: What if

  • Red Box : Green Balloons
  • Yellow Box: Blue Balloons
  • Blue Box: Red Balloons
  • Green Box: Yellow Balloon

Thus, we need to open minimum of 3 boxes to know what is contained in all the boxes"

Doesn't that makes sense?

I know the question asked for MINIMUM NUMBER OF BOXES, and if you'll look at the explanation, they have proved their answer. But what if there happens to be the case mentioned above?

Note by Daksh Gargas
4 weeks, 1 day ago

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1 vote

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No, it's still 2.

  1. You open the red box, which shows green balloons.
  2. You then open the green box, which shows yellow balloons.
  3. This means that blue box cannot contain green, yellow or blue balloons. So the blue box must contain red balloons.
  4. You're left with the yellow box which must contain blue balloons.

Pi Han Goh - 4 weeks, 1 day ago

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Why blue box can not contain yellow balloon? If you'll check the case 1 in the explanation, they have taken the assumption of "swapping the balloons"

Daksh Gargas - 4 weeks, 1 day ago

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Because the green box already contains yellow balloons, so the blue box cannot contain yellow balloons (again).

Pi Han Goh - 4 weeks, 1 day ago

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How can you be sure, what if green box contains red balloons? Don't you think in order to verify we need to check the third box?

Daksh Gargas - 4 weeks, 1 day ago

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@Daksh Gargas Suppose it's:

Red Box : Green Balloons
Yellow Box: Blue Balloons
Blue Box: Yellow Balloons
Green Box: Red Balloons

The answer is still 2.

  1. You open the red box, which shows green balloons.
  2. You then open the green box, which shows red balloons.
  3. This means that blue box cannot contain green, red or blue balloons. So the blue box must contain yellow balloons.
  4. You're left with the yellow box which must contain blue balloons.

Pi Han Goh - 4 weeks, 1 day ago

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@Pi Han Goh I totally agree with your solution but

If the order is Red Box : Green Balloons Yellow Box: Blue Balloons Blue Box: Red Balloons Green Box: Yellow Balloon

And the order of opening boxes is

1st: Red Box 2nd: Yellow Box

Then there is no way to figure out which colored balloon is present in Blue and Green box. Because it creates possibilities:

Blue box can contain : Yellow balloon or Red Balloon Similarly Green box can contain: Yellow balloon or Red Balloon

That's the only doubt I have.

Daksh Gargas - 4 weeks, 1 day ago

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@Daksh Gargas You shouldn't open the box in the given order.

And the order of opening boxes is

1st: Red Box 2nd: Yellow Box

Suppose you open the first box labeled colour X, and it shows that it contain balloons of colour Y, then open the second box with label colour Y. That way, you don't have to open the third box to figure out all the remaining colors.

Pi Han Goh - 4 weeks, 1 day ago

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