Logic Puzzles

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Show your work for each problem.

1.
Ana, Ben and Cleo each own one different pet: a cat, a dog or a fish. Ana's pet lives in water. Ben does not own the cat. Who owns the cat?
1. a)Ben
2. b)Cleo
3. c)It cannot be determined
4. d)Ana
2.
Mia, Tom and Leo are $10$ , $12$ and $14$ years old, one age each. Leo is the youngest. Mia is older than Tom. How old is Mia?
3.
Ana, Ben, Cleo, Dan and Eva line up by height, shortest first (position $1$ is the shortest). Cleo is the shortest. Ben is the tallest. Eva is taller than Ana but shorter than Dan. At which position is Eva?
4.
On the island of knights (always tell the truth) and knaves (always lie), which sentence can nobody ever say?
1. a)"I am a knight."
2. b) $2 + 2 = 4$
3. c)"I am a knave."
4. d) $2 + 2 = 5$
5.
Two whole numbers have a sum of $15$ and a difference of $3$ . What is the larger number?
6.
Ana, Ben and Cleo live in houses number $1$ , $2$ and $3$ , one house each. Ana does not live in house $1$ or house $3$ . Ben's house number is greater than Cleo's. In which house does Ben live?
7.
Three houses stand in a row: left, middle and right. They are painted red, blue and green, one color each. The red house is not in the middle. The green house is directly to the right of the red house. What color is the middle house?
1. a)It cannot be determined
2. b)Red
3. c)Green
4. d)Blue
8.
Eva, Leo, Mia and Tom stand in a line at positions $1$ (front) to $4$ (back). Tom stands directly behind Eva. Leo is not at either end. Mia stands somewhere behind Leo. At which position is Leo?
9.
Lea, Max and Sam ate $2$ , $3$ and $5$ slices of pizza, a different number each. Max ate more slices than Lea. Lea and Sam ate $7$ slices together. How many slices did Sam eat?
10.
On the island of knights (always tell the truth) and knaves (always lie), A says: "B is a knave." B says: "A and I are the same type." What are A and B?
1. a)A is a knave, B is a knight
2. b)A is a knight, B is a knight
3. c)A is a knight, B is a knave
4. d)A is a knave, B is a knave
11.
Six friends want to cross a river in a boat that holds at most $2$ people. The boat cannot cross empty, so someone must row it back each time. What is the smallest number of crossings? (Each one-way trip counts as one crossing.)
12.
On the island of knights (always tell the truth) and knaves (always lie), A says: "At least one of us two is a knave." How many knights are there among A and B?
13.
Two whole numbers have a sum of $11$ and a product of $24$ . What is the smaller number?
14.
Three boxes are labeled "Apples", "Oranges" and "Mixed". Every label is wrong. You may take one fruit out of one box without looking inside. From which box should you take it so that you can then label all three boxes correctly?
1. a)One fruit is never enough
2. b)The box labeled Apples
3. c)The box labeled Mixed
4. d)The box labeled Oranges
15.
A two-digit number has a digit sum of $12$ . If you swap its two digits, the new number is $18$ more than the original. What is the original number?
16.
Ana, Ben, Cleo and Dan live in houses $1$ , $2$ , $3$ and $4$ , which stand in this order along a street. Ben's house number is twice Ana's. Cleo lives right next door to Ben. Dan's house number is odd. In which house does Dan live?
17.
On the island of knights (always tell the truth) and knaves (always lie), A says: "B is a knave." B says: "C is a knave." C says: "A and B are both knaves." How many of the three are knights? In the steps, write $1$ for knight and $0$ for knave.
18.
Three adults and two children must cross a river. The boat can carry one adult, or one child, or two children, never more, and it cannot cross empty. What is the smallest number of crossings? (Each one-way trip counts as one crossing.)