A $20×20×20$ cube is built of $1×2×2$ bricks.Prove that one can pierce it by a needle without damaging one of the bricks.
2026-03-28 00:49:27.1774658967
A Question From Pigeon Hole Principle and Three Dimensional Tiling
140 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 $6$.
Related Questions in TILING
- Aperiodic tiles where the tiles are the same area?
- Is there a name for a set of elements that violate the conditions of the marriage theorem?
- Why is the "distributive lattice" structure of domino tilings significant?
- Coordinates of a plane tiling
- Unbounded, Repeated Figures in Non-periodic Tilings
- Have I explained that a tiled rectangle has at least one integer side properly?
- Trouble understanding tiling board with tiles of at least one integer dimension.
- tesselations in $1$ dimension (i.e., tiling a quotient group of integers with same-shaped subsets)
- Curve of fractal triangle.
- How many pair-wise touching "shapes" are there in an $n\times n\times n$ grid?
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?
It is possible to pierce such brick in 3 places, or through the center of $2 \times 2$ square, or through one of the two sides $1 \times 2$. How many possible ways are to pierce the cube? There are 3 different directions to pierce, each should pick one of the inner points in $20 \times 20$ field, otherwise it will pierce the first brick on its way.