## Brainteasers To Keep Your Mind Sharp

One of the best ways to prevent mental decline is to take some time every day to exercise your brain. As a public service, *Commonplace Fun Facts *offers you this opportunity to fire up those neurons so you will achieve tip-top mental shape.

**Question 1 — Which One is True?**

Only one of the following statements can be true. Which one is it?

- Exactly one of the statements in this list is false.
- Exactly two of the statements in this list are false.
- Exactly three of the statements in this list are false.
- Exactly four of the statements in this list are false.
- Exactly five of the statements in this list are false.
- Exactly six of the statements in this list are false.
- Exactly seven of the statements in this list are false.
- Exactly eight of the statements in this list are false.
- Exactly nine of the statements in this list are false.
- Exactly ten of the statements in this list are false.

The answer can be found at the bottom of the page.

**Question 2 — Another Where Only One Is True**

Only one of the following answers can be a true statement. Which one is it?

- All of the below.
- None of the below.
- All of the above.
- One of the above.
- None of the above.
- None of the above

The answer can be found at the bottom of the page.

**Question 3 — How Many Mistakes?**

How many mistakes are there in the sentence: ‘This sentance contanes one misteak’?

What is the answer to the same question for this sentence: ‘Their are three misteaks in this sentence’?

The answer can be found at the bottom of the page.

**Question 4 — Find the Next Number **

What is next in this sequence of numbers: 1, 11, 21, 1211, 111221, 312211, **__**?

The answer can be found at the bottom of the page.

**Question 5 — How Big Is Your Family?**

Your parents have six sons including you and each son has one sister. How many people are in the family?

The answer can be found at the bottom of the page.

**Question 6 — 2 Hourglasses, One Egg, and 15 **Minutes

You need to boil an egg for exactly 15 minutes. By way of timekeepers, you have only two instruments: an 11-minute hourglass and a 7-minute hourglass. Can you get the job done? If so, how?

The answer can be found at the bottom of the page.

How did you do? If you have a favorite brainteaser, or if you found a more creative way to solve any of these, send us an email or leave a comment at the bottom. We’d love to hear from you!

## ΑNSWERS

**Answer to Question 1**

The best way to figure this out is to restate each line in terms of what its logical consequence would be. For example, if the first statement, “exactly one of the statements in this list is false” is correct, that must mean that exactly nine of the statements in the list are true. If the second statement is correct, then exactly eight statements must be true. When viewed this way, since only one statement can be true, that means nine of them must be false. The correct answer is #9.

**Answer to Question 2**

Try looking for contradictions among the possible answers and eliminate them as you go:

- If 1 is true, then 2 must be true, but that would contradict 1, so 1 must be false.
- And if 1 is false, then 3 must be as well.
- If 2 is true, then 4, 5, and 6 must be false. But if 4 is false, it is not the case that only one of 1, 2, and 3 is true. This contradicts the premise, which is that 2 is true (and we know 1 and 3 are false). So 2 is also false.
- Since 1, 2, and 3 are false, so is 4.
- If 6 is true, 5 must also be true, but if 5 is true, then 6 is false. Therefore, 6 is false.
- 5 is true. It is, therefore, the correct answer.

**Answer to Question 3**

The sentence contains three spelling mistakes, and the premise of the sentence itself, that it only contains one mistake, is incorrect. The answer to the question is that it contains a total of four mistakes.

The second question, paradoxically, cannot be answered. It contains only two spelling mistakes but claims to contain three mistakes. Consequently, that claim is wrong, and it actually contains three mistakes. The problem is that if it contains three mistakes, then the claim that it contains three mistakes is correct, which would mean that it only contains the two spelling mistakes, etc.

**Answer to Question 4**

Each sequence of numbers is a verbal representation of the sequence before it. The sequence begins with a single numeral 1. It would be described as “one 1,” which is written as “11.” That is the second number in the sequence. The third number is derived by expressing the prior number, which consists of “two of numeral 1,” or “21.” The third number describes its predecessor, which is “one numeral 2 and one numeral 1” or “1211.” The answer, therefore, describes the number before the blank, which consists of “one numeral 3, one numeral 1, two numeral 2, and two numeral one,” or “13112221”.

**Answer to Question 5**

If each of the sons has only one sister, then there is only one daughter in the family. The answer is 9 — two parents, six sons, and one daughter.

**Answer to Question 6**

Yes, it can be done, provided you follow these steps:

- Start both hourglasses as you start boiling the egg.
- After the 7-minute hourglass runs out, turn it over to start it again.
- When the 11-minute hourglass runs out, it will be four minutes after you turned over the first hourglass. At that point, turn the 7-minute hourglass again.
- The newly-turned 7-minute hourglass has four minutes of sand remaining. When it runs out, exactly 15 minutes will have transpired.

Categories: Brainteasers and Puzzles

I found the first couple of these challenging… too much thinking involved!

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