If I have a set of 12 shirts comprised of 4 blue, 4 yellow, and 4 red shirts, how many shirts do I have to pick to ensure that there are at least 3 of one color?
2026-04-01 00:30:06.1775003406
Picking Colors of Shirts
54 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMBINATORICS
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
- Algebraic step including finite sum and binomial coefficient
- nth letter of lexicographically ordered substrings
- Count of possible money splits
- Covering vector space over finite field by subspaces
- A certain partition of 28
- Counting argument proof or inductive proof of $F_1 {n \choose1}+...+F_n {n \choose n} = F_{2n}$ where $F_i$ are Fibonacci
Related Questions in PIGEONHOLE-PRINCIPLE
- Is it possible to make a computer network of 75 computers
- Pigeonhole principle: prove that a class of 21 has at least 11 male or 11 female students.
- Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
- Question on proof of Erdos and Szekeres
- Pigeon Hole Principle Proof integrated with sets
- # of vertices and # of connected components proof problem?
- Prove that any collection of 8 distinct integers contains distinct x and y such that x - y is divisible by 7.
- Hint for problem on $4 \times 7$-chessboard problem related to pigeonhole principle
- Pigeonhole principle subsets
- $80$ balls in a row. $50$ of them are yellow and $30$ are blue. Prove that there are at least $2$ blue balls with a distance of exactly $3$ or $6$.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
What is the worst case scenario to not have at least three of a color?
If you pick one more shirt, are you guaranteed three of a color?
More generally, completely ignoring the number of each shirt available (as it is unnecessary information that plays absolutely no role in the solution to the question) the pigeonhole principle says that if you have $n$ objects divided into $k$ categories, you will necessarily have some category with at least $\lceil\frac{n}{k}\rceil$ objects in it.
Here, $k=3$ is the number of categories (the colors of shirts).
What is the smallest $n$ that works (number of shirts to select) so that $\lceil\frac{n}{3}\rceil \geq 3$?