# Reason + divisibility - math problems

1. Probability How probable is a randomly selected three-digit number divisible by five or seven?
2. Twenty-five How many three-digit natural numbers are divisible by 25?
3. Intelligence test Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, K
4. By six From the digits 1,2,3,4 we create the long integer number 123412341234. .. .. , which will have 962 digits. Is this number divisible by 6?
5. Sum of the digits How many are two-digit natural numbers that have the sum of the digits 9?
6. Math test In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?
7. Number What number should be placed instead of the asterisk in number 702*8 to get a number divisible by 6?
8. Red and white Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the opti
9. Twos Vojta started writing the number of this year 2019202020192020 into the workbook. .. And so he kept going. When he wrote 2020 digits, no longer enjoyed it. How many twos did he write?
10. Dance group The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
11. Three numbers We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?
12. Hens and pigs Hens and pigs have 46 feet in total. At least how much can heads have?
13. Reminder and quotient There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,
14. Six-digit primes Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
15. The Hotel The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
16. The florist The florist had 200 roses in the morning. During the day, more than half sold it. From the remaining roses, it will tie the bouquet. If a bouquet of 3, 4, 5 or 6 roses are bound, one always remains. How many roses from the morning shipment sold?
17. Chocolate I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
18. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
19. Four poplars Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
20. Odd/even number Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time. Prove. ..

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