Clan x86

Three boxes are labeled APPLES, ORANGES, and APPLES AND ORANGES. Each label is incorrect. Can you select one fruit from one box and determine the correct labels? If so, explain how.

You can't.

Let's say you have X, Y, and X+Y. If you pick one of the two X's (since you said only one fruit), you still have an X and two Y's. If you select one of the two Y's, you still have a Y left over and two X's.

Wrong ^^

I don't understand, could you rephrase? :O

All box's labels are false. You have to select one fruit from one box and determine the labels for each of the rest of them.

Yes.

Since the labels are false, draw from the A&O box. Which ever fruit comes out, that is the true label. (Let's say for clarity's sake, you draw an orange from the A&O box. Thus, this box is oranges.) (Since the label is false, whatever fruit you draw is the only fruit in the container!)

So we have: O labeled correctly, A&O unsure, A unsure.

Draw from the box labeled oranges (since you happened to pull an orange). If you pull an orange, this is the A&O box. If you pull an apple, this is the apple box.

Draw 1 fruit from box #2, and draw 1 fruit from box #3. One of two things will happen.

• Fruit from box #2/#3 will be orange. In this case, box #2/#3 = A&O and box #3/#2 = A
• Fruit from box #2 will be same as fruit from box #3. In this case, one of these boxes is labeled 'ORANGE' incorrectly. Whichever box you drew an apple from (that was labeled ORANGE) is the A&O box, and the other box is the apple box.

I almots got stuck twice there. Heh.

No.

QuoteAll box's labels are false. You have to select one fruit from one box and determine the labels for each of the rest of them.

QuoteSo we have: O labeled correctly, A&O unsure, A unsure.

No. ALL boxes are labeled INCORRECTLY.

Ohhh. Damnit.

Uh, ok.

• Draw from the A&O box. Let's say, you pull an orange out. This box is O.
• The box labeled apples is truly A&O. Since it can't have any apples, and you pulled oranges, it is A&O.
• You have box #3 as A because it's the leftover label.

The second part took a bit to think about. Hehe.

Good job. :)