Reason + divisibility - practice problems - page 5 of 10
Number of problems found: 188
- Hens and pigs
Hens and pigs have 46 feet in total. At least how much can heads have? - Reminder and quotient
There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S and D:S are with the remainder of 1. - The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals 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 - 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? - The florist
The florist had 200 roses in the morning. During the day, more than half sold it. The remaining roses will tie to the bouquet. One always remains if a bouquet of 3, 4, 5, or 6 roses is bound. How many roses from the morning shipment were sold? - 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 the ratio between white, milk, and dark chocolate. - 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? - Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Three-digit 7248
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. - Trees in alley
There are four trees in the alley between which the distances are 35m, 15m, and 95m. Trees must be laid in the spaces so that the distance is equal and maximum. How many trees will they put in, and what will be the distance between them? - MO C–I–1 2018
An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps? - Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - Clock's gears
In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position? - Notation 7014
There is no 0 in the decimal notation in natural numbers, and there are even numbers or odd numbers, each at least once. Find the number of all k-digit natural numbers. - Inverted nine
In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1,8,7,4,9? - PIN code
The PIN on Michael's credit card is a four-digit number. Michael told his friend: • It is a prime number - a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second digit is gre - 7 digit number
If 3c54d10 is divisible by 330, what is the sum of c and d?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.