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Number of problems found: 613
- Leader captain selection
How many ways can a 6-member football club member choose a leader and captain from among themselves? - Number 4
Camilla wrote all-natural numbers from 1 to 400 inclusive. How many times did she write the number 4? - Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere? - Deceleration of car
The car has a speed of 60 km/h and, after a 100 m journey speed of 40 km/h. What is the deceleration of a car if we assume that its movement is constantly slowed down? - Two-element combinations
Write all two-element combinations from elements a, b, c, and d. - Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice - Borrowing bicycle
Jacob lent a bicycle to friends who wanted to ride it. For a three-hour bike ride, Jacob received two chocolates. Yup. If you wanted a bike for 2 hours, you had to give Jacob 12 candies. Peter gave Jacob 1 chocolate and three candies. How long can Peter r - Number difference
Calculate the difference between the smallest odd four-digit number and the largest even three-digit number, where we can form each number from only these digits: 0, 1, 3, 5, 7, 8, 9 without repeating digits. - Tournament match calculation
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe? - Aleš coins
Alex has one coin, Boris and Cyril each have two coins. Aleš has 5 Sk more than Boris and 5 Sk less than Cyril. Note Czech coins are 1, 2, 5, 10, 20, 50 Sk. Aleš has ___ Sk. Boris has ___ Sk and ___ Sk. Cyril has ___ Sk and ___ Sk. Together, they have ___ - Natural number creation
How many natural numbers can you make from the digits in 4052? No digit may be repeated in the number entry. Sort the numbers in ascending order of size. - Divisible by nine How many three-digit natural numbers in total are divisible without a remainder by the number 9?
- Gold cube distribution
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3 cm, 4 cm, 5 cm, and 6 cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut.
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