# My Favorite Logic Puzzles

by John P. Pratt
last updated 15 Apr 2015

None of the following puzzles have trick answers, or unwarranted assumptions. They are arranged approximately in order of difficulty; the first few can be done by elementary school children, but they may need to be taught how to think. I tried to include a wide variety of types of puzzles, so that each would teach a new lesson in either logical thinking or finding creative solutions by breaking a variety of kinds of mental blocks. Moreover, most of them can be solved mentally by using a judicious point of view. Link to answers is found at the end, but don't go there until you've sweat plenty!

1. Brown, Jones and Smith are a doctor, a lawyer, and a teacher. The teacher, who is an only child, earns the least money. Smith, who married Brown's sister, earns more than the lawyer. What is each man's job?

2. A farmer has a fox, goose and a bag of grain, and one boat to cross a stream, which is only big enough to take one of the three across with him at a time. If left alone together, the fox would eat the goose and the goose would eat the grain. How can the farmer get all three across the stream without any of them being eaten?

3. A drawer contains 10 black and 10 brown socks that are all mixed up. What is the fewest number of socks you can take from the drawer without looking and be sure to get a pair of the same color?

4. There are three boxes which each contains two marbles: one has two white, one has two black and one has one white and one black marble. Each of the boxes also is labeled as to its contents, but each label is incorrect. What is the fewest number of marbles you could remove from the boxes and look at in order to definitely determine the contents of all three boxes?

5. When asked her 3 children's ages, Mrs. Muddled said that Alice is the youngest unless Bill is, and that if Carl isn't the youngest then Alice is the oldest. Who is the oldest and who is the youngest?

6. Two fathers and two sons went fishing. Each caught exactly one fish and yet there were only three fish caught. Why?

7. Mr. and Mrs. Smith and their two children form a typical American family. If exactly two of the following statements are true, what is the first name of the father, mother, son and daughter:

• George and Dorothy are blood relatives.
• Howard is older than George.
• Virginia is younger than Howard.
• Virginia is older than Dorothy.

8. Three men were standing in a row, all facing the same direction, so that there was one in back who could see the two in front of him, one in the middle, and one in front who could not see either of the other two. There were three blue and two red hats. One hat was placed on each man, without them seeing which two were left over. Each man was told the total number of each color of hat. First the man in the back was asked if he could deduce what color hat he had on, but he said he couldn't. Neither could the man in the middle, when he was next asked. But then man in the front, who could see neither of those behind him but could hear their answers, correctly deduced by logic what color hat he was wearing. What color was it and why?

Hint (point to "Hint" only if you are stumped.)

9. While a red mark was placed on the forehead of each of three blindfolded women seated facing each other in a circle, they were told that the the mark might be either red or white. Upon removal of the blindfolds, each was to raise her hand if she saw at least one red mark, and then to take it down if she could logically deduce the color of her own mark. All three hands were quickly raised, but then one of them lowered her hand. How did she know?

Hint (point to "Hint" only if you are stumped.)

10. [I received this puzzle in an email that said it was taken from a standardized test for 14-year-olds.] Albert and Bernard just became friends with Cheryl and they wanted to know her birthday. Cheryl gave them both a list of ten possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, Aug 14, Aug 15, and Aug 17. Cheryl then whispers the month to Albert and the day to Bernard.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know either.

Bernard: At first I didn't know when Cheryl's birthday is, but after hearing hearing Albert's statement, now I do know.

Albert: And now I also know when Cheryl's birthday is!

What is Cheryl's birthday?

Hint (point to "Hint" only if you are stumped.)

11. Mr. Reader's five daughters each gave books for Christmas to one or more of her sisters. Each presented four books and each received four books, but no two girls allocated her books in the same way. That is, only one gave two books to one sister and two to another. Beth gave all her books to Alice; Christy gave three to Edith. Which sisters gave the four books to Deborah?

12. How can you connect nine dots in three straight rows of three with four straight lines without raising the pencil from the paper?

13. A man needed to pay his rent and was out of money, but found that his rent was worth about one gold link on his chain per day. What is the fewest number of cuts he can make in his 23-link chain to pay the rent daily for up to 23 days?

14. An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?

15. A traveler meets a native in the jungle at a the fork in the trail, where only one path goes to the village. The traveler does not know which path to take and knows that the native could be either from the tribe of Truth-tellers, who always tell the truth, or from the Liars, who always lie. What is one question he could ask the native to discover the path to the village?

16. Twelve billiard balls all weigh the same, except for one that is either light or heavy. Determine in three weighings on a balance scale which is the "odd ball", and whether it is light or heavy.

17. A prisoner was given a chance to be blindfolded and pick one ball from two bowls that would contain a total of 50 white and 50 black balls. Choosing white meant freedom, black meant death. He asked if he could divide the balls between the bowls before he was blindfolded and his request was granted. What is the best way to divide the balls between the bowls?

18. How can three missionaries and three cannibals cross a river in a canoe that holds at most two people if the cannibals must never outnumber the missionaries on either side?

19. What is an English word that contains the five vowels a,e,i,o,u in order?

20. The following puzzle is about two actual historial people.

George and Evelyn never met but they carried on writing until late in life. It has been said that Evelyn loved George, but she was too old for him. George married in 1880. He converted to Catholicism in 1930. During World War II, he served with the Royal Marines. Partly in recognition of this, Evelyn's subsequent writings analyzed the character of that war.

Evelyn died in 1966 in Somerset. Her first full-length novel had been published in 1859. She is buried in Highgate Cemetery. He died at age 62, after having published his autobiography in 1964. He lived one year longer than she did.

How could these statements all be true?

21. The following is the only puzzle in this list which I created. It was a birthday gift for Brent, my nutty friend who reminds me of a big, rambling bear. Can you find his first, middle and last name spelled out in the verse, using a simple arithmetic code?

"Dizzy Bear" Brent: neater, no nuttiest
Brent; rambling,
Big and ageless.

Answers. No peeking until you've really sweat!