Integers + reason - practice problems - last page
Number of problems found: 60
- Positive integers
Several positive integers are written on the paper. Michaella only remembered that each number was half the sum of all the other numbers. How many numbers could be written on paper? - MO Z6-6-1
Write integers greater than 1 to the blanks in the following figure so that each darker box is a product of the numbers in the neighboring lighter boxes. What number is in the middlebox? - Report card
Ivor hit 4× grade 5 at the beginning of the school year. How many times must you now catch grade 1 to get grade 2 on the report card? - Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Integer cube
The length of the cube edge is an integer. Its volume is in cm3, a five-digit number divisible by 1331. What is the length of the edge of this cube? - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Sugar - cuboid
Pablo received from his master a cuboid composed of identical sugar cubes with a count between 1000 and 2000. The Pejko eat sugar cubes in layers. On the first day, eat one layer from the front. On the second day, one layer from the right, and on the thir - Dice
How many times must you throw the dice, and the probability of throwing at least one six was greater than 90%? - Three digits number
How many are three-digit integers such that they have no digit repeats? - Repairman
The repairman has vowed to do repair work at the plant for 25 days. However, work had to be shortened, so he took a helper worker. Together they made all the corrections for the whole day. How long would it take work to help workers? - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Non equivalent ints
Two n-digit integers are said to be equivalent if one is a permutation of the other. Find the number of 5-digit integers such no two are equivalent. If the digit 5,7,9 can appear at most one, how many non-equivalent five-digit integers are there? - Banknotes
$ 1390 was collected. How much was in $20 notes, and how many in $50 notes in that order? How many solutions exist? - Rectangles
How many different rectangles with sides integers (in mm) have a circumference of exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm) - Determine 5893
Determine the largest integer n for which the square table n×n can be filled with natural numbers from 1 to n² (n squared) so that at least one square power of the integer is written in each of its 3×3 square parts. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures are ignored. - Triangles
Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have? - Budapest 82510
In Trnava, it was -6 degrees Celsius; how much was it in Budapest, which was twice as hot.?
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