You have 10 baskets of apples. Each basket contains 10 apples. However, one of these baskets contains apples that each weigh 9 grams instead of the usual 10 grams. You have a highly accurate digital scale that you can use only once. The task is to determine which basket contains the lighter apples.

Objective:
Identify the basket with the lighter apples using the digital scale only once.

Solution

The key to solving this puzzle lies in using a clever strategy to weigh a specific number of apples from each basket so that the total weight will reveal the basket with the lighter apples.

Step-by-Step Solution for The Apple Basket Puzzle:

Step 1: Number the Baskets

Label the baskets from 1 to 10.

Step 2: Select a Specific Number of Apples from Each Basket

Take a different number of apples from each basket as follows:

• Take 1 apple from Basket 1.
• Take 2 apples from Basket 2.
• Take 3 apples from Basket 3.
• Continue this pattern until you take 10 apples from Basket 10.

Step 3: Weigh All the Selected Apples Together

Place all the selected apples on the digital scale at once and record the total weight.

Step 4: Calculate the Expected Weight

If all the apples were normal (weighing 10 grams each), the total weight would be:

• 1 + 2 + 3 + ... + 10 = 55 apples.
• Since each apple would weigh 10 grams, the expected weight would be 550 grams.

Step 5: Determine the Basket with Lighter Apples

Because one basket contains lighter apples (each weighing 9 grams), the total weight will be less than 550 grams. The difference between the expected weight (550 grams) and the actual weight will indicate which basket contains the lighter apples:

• If the total weight is 549 grams, then Basket 1 contains the lighter apples.
• If the total weight is 548 grams, then Basket 2 contains the lighter apples, and so on.

For example, if the total weight is 546 grams, the difference is 4 grams, meaning Basket 4 contains the lighter apples.

Final Answer

By following these steps, you can identify the basket with the lighter apples based on the difference between the expected and actual total weights.