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?
James spent the first Tuesday of some month in Liverpool and the first Tuesday after the first Monday he spent in Newcastle. In the next month, James spent the first Tuesday in Dover and the first Tuesday after the first Monday he spent in Bristol. Could you determine the dates (day and month) spent by James in each of the cities?
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.
Harry, Jack and Fred were seated so that Harry could see Jack and Fred, Jack could only see Fred, and Fred could not see anyone. Then, from a bag which contained two white caps and three black caps (the contents of the bag were known to the boys), they took out and each put on a cap of an unknown color, and the other two hats remained in the sack. Harry said that he could not determine the color of his hat. Jack heard Harry’s statement and said that he did not have enough information to determine the color of his hat. Could Fred on the basis of these answers determine the color of his cap?
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?