On the table four figures lie in a row: a triangle, a circle, a rectangle and a rhombus. They are painted in different colors: red, blue, yellow, green. It is known that the red figure lies between the blue and green figures; to the right of the yellow figure lies the rhombus; the circle lies to the right of both the triangle and the rhombus; the triangle does not lie on the edge; the blue and yellow figures are not next to each other. Determine in which order the figures lie and what colors they are.
One day a strange notebook was found on the stairs. It contained one hundred statements:
“There is exactly one incorrect statement in this notebook”;
“There are exactly two incorrect statements in this notebook”;
“There are exactly three incorrect statements in this notebook”;
...
“There are exactly one hundred incorrect statements in this notebook.”
Are any of these statements true, and if so, which ones?
Dave spent the first Tuesday of the month in Bath, and the first Tuesday after the first Monday in Cardiff. The following month Dave spent the first Tuesday in London, and the first Tuesday after the first Monday in Cambridge. Can you determine what month and date Dave was in each of the cities?
Once Alice was in one of two countries – A or Z. She knows that all of the residents of country A always tell the truth, and all the inhabitants of country Z always lie. Moreover, they often go to visit each other. Can Alice, after asking a single question to the first person that she meets, find out which country she is in?
In a cup, glass, jug and jar there is milk, lemonade, cola and water. It is known that the water and the milk are not in the cup; the container with the lemonade stands between the jug and the cola container; the jar does not contain lemonade or water; the glass stands near the jar and the container with milk. Which container is filled with each of the liquids?
When three friends – Nina, Helen and Anna – went out for a walk, they were wearing white, red and blue dresses. Their shoes were of the same three colors, but only Nina had the same shoe and dress color. At the same time, neither Helen’s dress, nor her shoes were blue, and Anna was wearing red shoes. Determine the color of the dresses and of the shoes of each friend.
Five first-graders stood in line and held 37 flags. Everyone to the right of Harley has 14 flags, to the right of Dennis – 32 flags, to the right of Vera – 20 flags and to the right of Maxim – 8 flags. How many flags does Sasha have?
The Olympic gold-medalist Greyson, the silver-medalist Blackburn and bronze-medalist Reddick met in the club before training. “Pay attention,” remarked the black-haired one, “one of us is grey-haired, the other is red-haired, the third is black-haired. But none of us have the same colour hair as in our surnames. Funny, is not it?”. “You’re right,” the gold-medalist confirmed. What color is the hair of the silver-medalist?
On the street, four girls are talking in a circle: Anna, Kate, Jane and Nina. The girl in the green dress (not Anna and not Kate) stands between the girl in the blue dress and Nina. The girl in the white dress stands between the girl in the pink dress and Kate. What color dress was each girl wearing?
Two tribes live on the island: natives and newcomers. It is known that the natives always tell the truth and the newcomers always lie. A traveler hired an indigenous islander as a guide. On the way, they met a man. The traveler asked the guide to find out which tribe this person belongs to. The guide returned and said that the man said that he was a native. Who was the guide – a native or a newcomer?