Prime numbers - practice problems - page 8 of 23
Number of problems found: 458
- Wedding guests
Fifteen wedding guests could not agree on who would stand in the wedding photo. The groom suggested that all possible sets of wedding guests be made in the photographs. - Two gears
Two gears with 13 and 7 teeth rotate locked into each other. We want both wheels to be in the starting position again. How many turns does a big wheel have to make? - Three ships
There are three ships moored in the port, which sail together. The first ship returns after two weeks, the second after four weeks, and the third after eight weeks. In how many weeks will the ships meet in the port for the first time? How many times have - Non-repeating 30101
1. How many different options are there for exchanging a ten-euro bill with one-euro, two-euro, and five-euro bills? a) 5 b) 8 c) 14 d) 10 2. How many non-repeating three-digit numbers can be written using odd digits? a) 999 b) 225 c) 60 d) 25 - Different 29943
Vojta added five different prime numbers to the top row of the census pyramid. Their sum was 50. What was the biggest number he could get "down"? - Probability 28111
1. What is the probability that we write an even number from the numbers from 1 to 20? 2. We randomly draw one ticket From the eighteen tickets numbered 1 - 18. What is the probability that the ticket drawn will have: a) a number divisible by 3 c) a prime - Returning 27121
Two gears – one smaller and one larger rotate so that the teeth of both wheels mesh together. The first wheel has 18 teeth, the second 27. How often does each wheel turn before returning to its starting position? - Intervals 27081
Three lines depart from the bus terminal at 5:30 in the morning. At what time will all three buses meet again at the terminus first, if one has intervals of 10 minutes, the second 12 minutes, and the third 15 minutes? - Lamps on playground
The playground has the shape of a rectangle of 36 x 50m. After how many meters can place the lamps on its lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps? - Divisors of 560
Which of the numbers 5, 6, 7, 14, and 15 are divisors of 560? Please justify the answer. - The missing digit
Complete the missing digit in the number 3 ∗ 43 to form a number divisible by three. If there are multiple options, list them all. (The omitted digit is marked with the symbol ∗. ) Answers must be justified! - Prime factors
Factor the number 6600 into the product of prime numbers. - Ratio
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order. - Simultaneously 25521
People travel to the seaside in Greece for 8-day, 10-day and 12-day stays. An assigned delegate flies there and back with each group of passengers. On May 1, all three groups and their delegates will fly to the sea simultaneously. When will all three dele - On a
On a someday, the Sun, Venus, and the Earth are in eclipse, i. E. Venus is 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? - Drivers
Driver Franta and driver Karel are friends. They leave the start-stop at the same time in the afternoon - at 13.30. When will they meet again if Franta goes around his route in 50 minutes and Karel in 40 minutes? - Revolutions 24121
The white wheel has 24 teeth. The black wheel has fewer teeth than the white wheel. Both wheels return to their initial position for the first time after two revolutions of the white wheel. How many teeth does the black wheel have? - Diameters: 23901
When paying, we use euro coins with the following diameters: The 10-cent coin has a diameter of 19.75 mm. The 20-cent coin has a diameter of 22.25 mm. The 50-cent coin has a diameter of 24.25 mm. Find out in what ratio the diameters of these coins are. - Dividing nuts
How many nuts do you have when dividing them between 2, 3, 4, 5, 6, 8, and 10 children? (smallest possible number) - Tram stop
The blue tram stops every 12 minutes, the red one for 8 minutes. At 8 o'clock, they left the stop together. How many times do they meet at a stop before 11 AM?
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