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Number of problems found: 1877

Triangle from sticks
Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks?
Counting hairs
Find out if two people in Bratislava have the same number of hairs on their heads. Instructions. Bratislava has about 420,000 inhabitants, and a person has less than 300,000 hairs on his head.
Nine-digit numbers
Determine the number of nine-digit numbers in which each of the digits 0 through 9 occurs at most once and in which the sums of the digits 1 through 3, 3 through 5, 5 through 7, and 7 to the 9th place are always equal to 10. Find the smallest and largest
Employee reduction probability
Seven women and 3 men work in one office. According to the new regulation, reducing the number of employees by three is necessary. In a random sample of employees, what is the probability that they will be fired: a. One woman and two men b. At least one w
Two buses
The first bus runs for 15 minutes, and the second bus runs after 21 minutes. Together, they both leave at 7:00 on Monday. When and what day will they meet?
Container
The container-shaped box with internal dimensions of 3.9 m, 3.25 m, and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
Triangles
Ivo wants to draw all the triangles whose two sides have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have?
Room people capacity
The room is 240 cm high and has a volume of 48 m³. How many people can work in it when there is 7 m² of floor space per person?
Multiple-choice
A multiple-choice test consists of 4 questions. Each question has three different answers, with only one being correct. A student answers each question randomly. Determine the expected number of correct answers the student gets.
Karel grade average
Charles has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one.
Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7, and 8, wherein on different sides are different numbers. John makes the sum of the numbers written on three adjacent walls for each wall. Thus got eight sums, which al
Number divisibility probability
What is the probability that any two-digit number a) is divisible by five b) is it not divisible by five?
Gear train
A gear train is assembled from three gear wheels. The first has 165 teeth, the second 132 teeth, and the third 231, where the second engages with the first and the third with the second. The first and third do not touch. How many times per minute will all
Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
Dining room lineup
If the boys let the two girls in front of them, how many different ways can Annie, Betty, Cyril, Daniel, and Eric line up in the dining room?
Three-digit number
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number.
On a
Someday, the Sun, Venus, and the Earth will be in eclipse, i.e., Venus will be between the Sun and the Earth. Venus orbits the Sun in 225 days. In how many years will all three bodies be in alignment again?

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