A cake is decorated with berry and caramel flavoured sweets so that they go around the outer edge of it in a circular fashion. There are 2B berry-flavoured sweets and 2C caramel sweets in some order around the boundary of the cake. You want to divide your cake in half, in such a way that each half has B berry sweets and C caramel sweets. Can you always do this, no matter how the berry and caramel sweets are ordered?
2026-03-25 15:56:43.1774454203
A problem about a cake...
87 Views Asked by user266729 https://math.techqa.club/user/user266729/detail At
1
There are 1 best solutions below
Related Questions in RECREATIONAL-MATHEMATICS
- Good ideas for communicating the joy of mathematics to nine and ten year olds
- Who has built the house of Mason?
- Is there any tri-angle ?
- In what position , the dogs will reside?
- existence of solutions of $a^n+b^n+c^n=6^n$
- Sushi Go! and optimal passing strategy
- Cut the letter $M$ to obtain $9$ single triangles by drawing $3$ straight lines
- Tennis balls problem from John H Conway's "Genius At Play"
- The Heegner Polynomials
- 2018 January Challenge: Prove inequality in geometry problem
Related Questions in PROBLEM-SOLVING
- How do you prevent being lead astray when you're working on a problem that takes months/years?
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- How to solve higher order polynomial equations?
- Methods in finding invariant subspaces?
- Question about the roots of a complex polynomial
- Using a counting argument to prove some equalities? (Problem Solving)
- (Problem Solving) Proving $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\frac{1}{k+m+1}=\sum_{k=0}^{m}(-1)^k\binom{m}{k}\frac{1}{k+n+1}$
- (Problem Solving) Proving $|x|^p +|y|^p \geq |x+y|^p$
- Each vertex of the square has a value which is randomly chosen from a set.
- Fill in the blanks
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?
Start at a cut in half that minimizes the count of berry sweets on a chosen half, call the count $x$. By moving the cut along a single sweet there are three possibilities either $x$ stays the same, decreases by 1 or increases by 1.
Now note by the time we have gone half way round the cake we will have gone from $x$ berry sweets on the chosen half to $2B - x$ sweets on a half so in this process at some point we must have had exactly B sweets on the half.