Reason + exponentiation - practice problems
Number of problems found: 22
- Seven segments display
Electronic devices sometimes use the type of digits below, where each digit uses some short stripes. For example, seven uses three small stripes. What is the largest three-digit number that you can make if you use twenty stripes? - Regularly 46301
Mišo will start regular morning exercise on the first of January. Once he gets up, he squats regularly. Every next day he does twice as many squats as the previous day. On which day will he do sixteen times as many squats as he did on the third day? - Before yesterday
The merchant adds a sale sign in his shop window to the shown pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the - The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets and their products was the power of the prime number. Find all possible ticket prices.
- 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. - Last digit
What is the last number of 2016 power of 2017 - Divisors 6619
Which natural number less than 100 has the largest number of divisors? - Multiply 6257
If we multiply the numbers of the last three pages of the book on pyramids, we get the product 23639616. How many pages does the book have if the last page's number is steam? - Disembarked 5962
Twenty-two passengers boarded in Žilina. Everyone gradually disembarked on the Teplička, Strečno, Vrútky, and Martin lines (the wagon was already empty in Martin). How many ways could they come out?
- Big number
What is the remainder when dividing 10 by 9 to 47 - 111? - Asymmetric 5407
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121) - Doubling
The message is spreading that each day has doubled the number of people who know about it. All know a message for 20 days. How long known it, eighth people? - Z9-I-4
Kate thought of a five-digit integer. She wrote the sum of this number and its half in the first line of the workbook. On the second line, write a total of this number, and its one fifth. She wrote a sum of this number and its one nines on the third row. - Multiply 3766
Peter had a number in mind and said: When I divide this unknown number by the square root of 27 and then multiply by three, I get an unknown number. What number did Peter think?
- Represents 3753
Dana and Julka's numbers are different. Dana's number represents the eleventh root of Julkin's number. The sum of their numbers is 2050. Determine what number Dana has and what Julka has. - Medicine
We test medicine on six patients. For all, the drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work? - Digits A, B, C
For the various digits A, B, and C is true: the square root of the BC is equal to the A, and the sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product). - Motion problem
From Levíc to Košíc, go car at speed 81 km/h. From Košíc to Levíc, go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away? - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately?
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