All Questions ⁺⁰237417 Questions

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+458

Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry Apr 19, 2025

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3

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+608

Counting

Adam the ant starts at (0,0). Each minute, he flips a fair coin. If he flips heads, he moves 1 unit up; if he flips tails, he moves 1 unit right.
Betty the beetle starts at (1,1). Each minute, she flips a fair coin. If she flips heads, read more ..

onyuIee Apr 19, 2025

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+608

Counting

Consider the sequence
1, 5, 6, 25, 26, 30, 31, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 5.
What is the first term that is greater than 50?

onyuIee Apr 19, 2025

0

3

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+608

Counting

Consider the sequence
1, 3, 4, 9, 10, 12, 13, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 3.
What is the first term that is greater than 20?

onyuIee Apr 19, 2025

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+1800

Counting

Find the number of sequences containing three terms, such that
* The second term is equal to the sum of the first term plus one.
* The third term is equal to twice the second term.
* Each term is an integer in \{0, 1, 2, \dots, 100\} read more ..

blackpanther Apr 19, 2025

Apr 18, 2025

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1

+56

Counting

Find the number of arithmetic sequences such that:
* The arithmetic sequence contains three terms
* All the terms are integers in \{0, 1, 2, \dots, 10\}
* The sum of the terms is 9.

PikaPika989 Apr 18, 2025

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+56

Counting

Find the number of paths from A to B in the grid below, where each step is down or to the right.
The grid is 3 by 3, with A in the upper-left and B in the lower-right.

PikaPika989 Apr 18, 2025

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+56

Counting

A basket contains 7 green marbles and 6 red marbles. Two marbles are taken from the basket at random without replacement (i.e., the first marble is not put back before the second marble is drawn). What is the probability that the first marble is green, read more ..

PikaPika989 Apr 18, 2025

Apr 17, 2025

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+357

Counting

In the United States, there are 50 states. Each state is represented by 2 senators. In how many ways can we form a committee with 5 senators, in which no two of the senators are from the same state?

cwimie Apr 17, 2025

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+357

Counting

Suppose for this problem (though it may not be accurate in real life) that the Senate has 48 Republicans and 52 Democrats. In how many ways can we form a committee with 5 senators, in which neither party holds all 5 seats?

cwimie Apr 17, 2025

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+56

help with counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

PikaPika989 Apr 17, 2025

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+56

Counting

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

PikaPika989 Apr 17, 2025

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1

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+56

Counting

In how many ways can 5 balls be placed in 4 boxes, if 2 balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

PikaPika989 Apr 17, 2025

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+56

help with counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

PikaPika989 Apr 17, 2025

+1

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+16

Help Please Intermediate Algebra

The range of the function is . Let . Find the range of the function .
Thanks!

PikaPika999 Apr 17, 2025

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+806

Counting

Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.

crimefightingvigiI Apr 17, 2025

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1

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+958

Counting

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

gnistory Apr 17, 2025

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+958

Counting

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

gnistory Apr 17, 2025

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+22

Using Geo/Trig on an Algebra Problem

What is $xy+yz+xz$ if $x^2+xy+y^2=1$, $y^2+yz+z^2=2$, and $x^2+xz+z^2=3$?

Xenosmilus Apr 17, 2025

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+458

Counting

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with read more ..

bIueb3rry Apr 17, 2025

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+458

Counting

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

bIueb3rry Apr 17, 2025

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+458

Counting

How many ordered pairs of positive integers (m,n) satisfy \text{lcm}[m,n] = 360 and \gcd(m,n) = 360?

bIueb3rry Apr 17, 2025

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+458

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that read more ..

bIueb3rry Apr 17, 2025

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+400

Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds read more ..

Stanry Apr 17, 2025

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