Squares and Square Roots | A

Question 4

There are 3 closed boxes—one containing only red balls, the second containing only blue balls and the third containing only green balls. The boxes are labelled RED, BLUE and GREEN such that ‘no’ box has the correct label. We need to find which label goes with which box. How can this be done if we are allowed to open only one box?

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Solution

Since no box has the correct label, we can use this information to find the true contents of each box by opening just one.

Step 1 — Choose a box to open

We know that every box has the wrong label. This means the box labelled RED does not contain red balls. It means the box labelled BLUE does not contain blue balls. It means the box labelled GREEN does not contain green balls. Let us choose to open the box labelled RED. We will take out one ball from this box.

Diagram 1

Step 2 — Deduce contents if a Blue ball is found

Suppose we open the box labelled RED. We find a blue ball. This means the box labelled RED contains blue balls. Now we know the contents of one box. Let us consider the box labelled BLUE. It cannot contain blue balls, because the RED box has them. It also cannot contain its own colour, blue, due to the given rule. So, the box labelled BLUE must contain green balls. This leaves only one type of ball (red) and one box (labelled GREEN). The box labelled GREEN cannot contain green balls, due to the given rule. It cannot contain blue balls, because the RED box has them. So, the box labelled GREEN must contain red balls.

If RED box has Blue: RED = Blue, BLUE = Green, GREEN = Red\boxed{\text{If RED box has Blue: RED = Blue, BLUE = Green, GREEN = Red}}

Step 3 — Deduce contents if a Green ball is found

Suppose we open the box labelled RED. We find a green ball. This means the box labelled RED contains green balls. Now we know the contents of one box. Let us consider the box labelled BLUE. It cannot contain green balls, because the RED box has them. It also cannot contain its own colour, blue, due to the given rule. So, the box labelled BLUE must contain red balls. This leaves only one type of ball (blue) and one box (labelled GREEN). The box labelled GREEN cannot contain green balls, due to the given rule. It cannot contain red balls, because the BLUE box has them. So, the box labelled GREEN must contain blue balls.

If RED box has Green: RED = Green, BLUE = Red, GREEN = Blue\boxed{\text{If RED box has Green: RED = Green, BLUE = Red, GREEN = Blue}}

Answer

(i) Open the box labelled RED and take out one ball. (ii) If the ball is blue, then the box labelled RED has blue balls, the box labelled BLUE has green balls, and the box labelled GREEN has red balls. (iii) If the ball is green, then the box labelled RED has green balls, the box labelled BLUE has red balls, and the box labelled GREEN has blue balls.

More questions in A

Q1

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Q2

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Q3

Will the square having half the sidelength have half the area? Why not? How many such squares will fill the original square?

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Q4

There are 3 closed boxes—one containing only red balls, the second containing only blue balls and the third containing only green balls. The boxes are labelled RED, BLUE and GREEN such that ‘no’ box has the correct label. We need to find which label goes with which box. How can this be done if we are allowed to open only one box?

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