Natural numbers + reason - practice problems - page 26 of 28
Number of problems found: 543
- Five-digit numbers
How many different five-digit numbers can be created from the number 2,3,5 if the number 2 appears in the number twice and the number 5 also twice? - Three-digit 9531
How many three-digit numbers do not change if we replace the digit in the hundreds with the digit in the units? - Balls in row
Calculate the number of ways of placing four black balls, four turquoise balls, and five gold balls in a row. - A bag
A bag contains nine blue marbles and one green marble. What is the probability of drawing a blue marble followed by a green marble without replacing the first marble before drawing the second marble?
- 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. - Three digits number
From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there? - Chocolates
In the market, we have 3 kinds of chocolates. How many ways can we buy 8 chocolates? - Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product.
- Fruits
The shop sells four kinds of fruits. How many ways can we buy three pieces of fruit? - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - Permutations 82516
From how many elements can we make 5040 permutations without repetition? - 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.) - Competition 33041
The long-term volleyball tournament is played on a one-on-one basis. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe?
- Paving - joints
We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and the second row in width etc. How many times will the joints meet at a distance of 10 m? - 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? - Justification 8468
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Directly 55591
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Differences 80551
Bolek and Lolek each had their own arithmetic sequence. Both Lolek and Bolek's sequence started with the number 2023 and ended with the number 3023. The two sequences had 26 numbers in common. The ratio of Bolek's and Lolka's difference was 5:2. What is t
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