# Can you solve it? I've got a little (logical) list

Puzzles that make a statement

UPDATE: The solutions can now be seen here.

Hi guzzlers,

(i) People who are logically minded like to list things.

(ii) These two logic puzzles celebrate this fact.

ONE

Which of the following statements is/are true?

1. Exactly one of the statements in this list is false.

2. Exactly two of the statements in this list are false.

3. Exactly three of the statements in this list are false.

4. Exactly four of the statements in this list are false.

5. Exactly five of the statements in this list are false.

6. Exactly six of the statements in this list are false.

7. Exactly seven of the statements in this list are false.

8. Exactly eight of the statements in this list are false.

9. Exactly nine of the statements in this list are false.

10. Exactly ten of the statements in this list are false.

TWO

Which answer in the list is the correct answer to this question?

1. All of the below.

2. None of the below.

3. All of the above.

4. One of the above.

5. None of the above.

6. None of the above.

I’ll be back at 5pm UK time with the solutions and explanations.

UPDATE: read the solutions here.

The first problem is included in Making Up Your Own Mind: Thinking Effectively through Creative Puzzle-Solving by Edward B Burger, which is out later this year. Burger is a brilliant mathematical educator from Texas, and his book has a stylistic innovation: the solutions are printed in mirror writing. Burger writes that this is to “challenge the reader to see the world through different perspectives”. But it’s also a great impediment to looking up the answer as soon as you get stuck. Unless you have a mirror at hand you won’t be able to read it.

NO SPOILERS PLEASE. (Although since inevitably someone will ignore this appeal, if you want to work on the problem with no help, to be safe DO NOT SCROLL BELOW THE LINE!)

But feel free to discuss (and suggest new) logic list puzzles, and your favourite lines from Gilbert and Sullivan.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja.

Alex Bellos

The Guardian

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