Natural numbers - math word problems - page 87 of 91

Number of problems found: 1816

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.)
Three-digit 67834
The number 0,3,7,4 are given. How many three-digit numbers are there: a) if the numbers can be repeated b) if the numbers cannot be repeated c) how many even three-digit numbers if the numbers can be repeated d) how many odd three-digit numbers if the num
Tournament 61544
In an amateur chess tournament, everyone plays with everyone. There are a total of 171 chess games on the program. How many players take part in the match?
Binary words
How many 10-bit words can be created with precisely four units (e.g., 1111000000)?
Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption do we start?
Bed 10
A bed shaped like two equilateral triangles with a common side, with a side length of 2.5 m, is to be planted with seedlings of an ornamental shrub. The gardener recommended leaving 40 cm between the individual seedlings and 10 cm of the perimeter for the
Students 36881
As a reward, the trip's land is ten students from a class of 25 students. How many options are there?
Three-digit 67824
The numbers 1,3,7,4 are given. How many three-digit numbers are there: a) if the numbers can be repeated b) if the numbers cannot be repeated c) how many even three-digit numbers if the numbers can be repeated d) how many odd three-digit numbers if the nu
Assembling 63964
Little Pavel was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit?
Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400?
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.
The gems
The jeweler selects four gems for the ring: rubies, emeralds, and sapphires. How many options does he have?
A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 7.
Permutations 82516
From how many elements can we make 5040 permutations without repetition?
Numbers 6D
Find out how many natural six-digit numbers exist whose digit sum is four.
How many 13
How many ways can X³ y⁴ z³ be written without an exponent?
Arithmetic 62644
The sum of the two numbers is 18, and their difference is 10. What are the numbers? Calculate the arithmetic mean of the product and the proportion of these numbers.
No. of divisors
How many different divisors have number 13⁴ * 2⁴?
Competition 33041
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe?
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?

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