GEOMETRY

DIVIDE THE TRAPEZOID INTO TWOHow can you divide the trapezoid into two parts so that after being folded,they will form a triangle? CUTTING THE FIGURE INTO THREEA plane figure consists of two squares such that AB = BC (see figure).Divide the figure with two perpendicular cuttings so that after translation ofthe three parts, they form […]

EQUATIONS

THE CHINESE AND THEIR BICYCLES. In a certain Chinese village live 29 families. Each family has one, two or three bicycles. There are as many families owning three bicycles as families with only one. How many bicycles are there in the village?

NATURAL NUMBERS AND INTEGERS

AQUARIUM.A cuboidal glass aquarium filled to the brim with water weighs 108 lb. The very same vessel half filled weighs 57 lb. How much does the empty aquarium weigh? THE YEAR OF SOPHIE’S BIRTH.In January 1993, Sophie’s age equaled the sum of digits comprised in her birth year. What year was Sophie born in? A […]

DIVISIBILITY AND PRIME NUMBERS

MR. T’S SONS. The age of each of Mr. Triangle’s three sons is an integer. The sum of these integers equals 12, and their arithmetic product is 30. How old is each of Mr. Triangle’s sons? A ONE HUNDRED-HEADED DRAGON. Once upon a time, there lived a fierce dragon, which had a hundred heads. With […]