Natural numbers - high school - practice problems - page 16 of 17
Number of problems found: 324
- Triangular numbers
The first four triangular numbers are 1,3,6,10. What is the 10th triangular number? Help: A triangular number or triangle number counts objects arranged in an equilateral triangle. - The sum
The sum of the first ten members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2? - Find x 2
Find x, y, and z such that x³+y³+z³=k for each k from 1 to 100. Write down the number of solutions. - Decreasing 36183
Prove that the sequence {3 - 4. n} from n = 1 to ∞ is decreasing.
- Other's 31461
There are 13 guests at each other's party. How many clicks will you hear? - Dimensions 7912
How many blocks have integer dimensions of the edges of the surface is 48 m²? - 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. - Ten persons
Ten persons, each person, make a hand to each person. How many hands were given? - 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
- 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 - Z9–I–1
In all nine fields of given shape to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in th - 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? - Four digit codes
Given the digits 0-7. If repetition is not allowed, how many four-digit codes that are greater than 2000 and divisible by 4 are possible? - Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2).180 degrees.
- Triangle from sticks
Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks? - Probability 71204
On ten identical cards, there are numbers from zero to nine. Determine the probability that a two-digit number randomly drawn from the given cards is: a) even b) divisible by six c) divisible by twenty-one - Determine 55891
Determine the number of nine-digit numbers in which each of the digits 0 through 9 occurs at most once and in which the sums of the digits 1 through 3, 3 through 5, 5 through 7, and 7 to the 9th place are always equal to 10. Find the smallest and largest - Instructions 10282
Find out if two people in Bratislava have the same number of hairs on their heads. Instructions. Bratislava has about 420,000 inhabitants, and a person has less than 300,000 hairs on his head. - Probability 38041
Seven women and 3 men work in one office. According to the new regulation, reducing the number of employees by three is necessary. In a random sample of employees, what is the probability that they will be fired: a. One woman and two men b. At least one w
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