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Forums
Mathematics
General Math
MHB Math Problem of the Week
Math POTW for Secondary and High School Students Forum
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MHB
Can Complex Equation |z|=1 Be Proven for 11z^10+10iz^9+10iz-11=0?
May 23, 2018
Replies
1
Views
1K
MHB
Can Exponents Reveal Which Fraction is Greater?
May 15, 2018
Replies
1
Views
975
MHB
How Does Air Resistance Affect a Fire Helicopter's Bucket?
May 8, 2018
Replies
1
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1K
MHB
Electric Field Zero: Charge Distribution on Y-Axis
May 2, 2018
Replies
1
Views
984
MHB
Choosing the Right Force: Bug Survival Odds on a Frictionless Table
Apr 26, 2018
Replies
1
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1K
MHB
What Power is Needed for Sinusoidal Waves in a Taut Rope?
Apr 20, 2018
Replies
1
Views
938
MHB
Can You Prove This Factorial Inequality for All Positive Integers?
Apr 12, 2018
Replies
1
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1K
MHB
Probability of Midpoint in Set S | POTW #307 Mar 28th, 2018
Apr 6, 2018
Replies
1
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1K
MHB
Is \(n^{n+1} > (n+1)^n\) for All \(n \geq 3\)?
Mar 28, 2018
Replies
1
Views
1K
MHB
What Is the Minimum Sum of $a+b+c+d+e+f+g$ Given Their Progressive Inequalities?
Mar 22, 2018
Replies
1
Views
1K
MHB
How Do You Solve Complex Series Without a Calculator?
Mar 14, 2018
Replies
2
Views
1K
MHB
What is the Minimum Value of Sum of Squares for Real Numbers in this POTW?
Mar 7, 2018
Replies
1
Views
1K
MHB
Convex Quadrilateral Problem: Prove Inequality with Diagonal Point T
Feb 28, 2018
Replies
1
Views
895
MHB
Can you solve these quadruple equations with real numbers?
Feb 21, 2018
Replies
2
Views
1K
MHB
What are the possible values of 1/a + 1/b when a^3+3a^2b^2+b^3 = a^3b^3?
Feb 13, 2018
Replies
1
Views
1K
MHB
Triangle ABC: Prove cot(A/2) + cot(C/2) = 2cot(B/2)
Feb 6, 2018
Replies
1
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1K
MHB
What is the sum of the angles in a right triangle?
Jan 30, 2018
Replies
1
Views
1K
MHB
What Is the Product of (1+k) for All Roots of a 15th Degree Polynomial?
Jan 24, 2018
Replies
1
Views
1K
MHB
What Is the Smallest Integer $a$ for $\frac{1}{640}=\frac{a}{10^b}$?
Jan 17, 2018
Replies
1
Views
948
MHB
How to Maximize the Product ab Given Specific Square Root Conditions?
Jan 10, 2018
Replies
1
Views
1K
MHB
Prove Inequality: (x^2+y^2+z^2)(x+y+z) + x^3+y^3+z^3 > 4(xy+yz+zx)
Jan 2, 2018
Replies
1
Views
962
MHB
Integers as Roots of Polynomial: Find Possible Values | POTW #293 Dec 19th, 2017
Dec 26, 2017
Replies
2
Views
1K
MHB
How Can You Minimize This Complex Fraction Given the Constraints?
Dec 19, 2017
Replies
1
Views
1K
MHB
What Is the Minimum Value of This Complex Fractional Expression?
Dec 10, 2017
Replies
1
Views
1K
MHB
Can You Solve the Existence of $x$ in this Trigonometric Equation?
Dec 3, 2017
Replies
1
Views
1K
MHB
Can You Solve High School POTW #289's Trigonometric and Polynomial Equation?
Nov 25, 2017
Replies
1
Views
1K
MHB
Solution to Quadratic Expression with Three Distinct Real Numbers
Nov 25, 2017
Replies
1
Views
1K
MHB
How Do You Solve POTW #287 Involving Integer Equations?
Nov 18, 2017
Replies
1
Views
1K
MHB
Tricky Trigonometry: Evaluating Cosine Cubes Without a Calculator
Nov 13, 2017
Replies
1
Views
1K
MHB
How Do You Prove the Root Constraints of a Quadratic Equation Given a Summation?
Nov 5, 2017
Replies
1
Views
1K
MHB
What are the real numbers that give positive integer roots for a cubic equation?
Oct 28, 2017
Replies
1
Views
1K
MHB
Can You Prove This Reciprocal Sequence Sum is Less Than 4?
Oct 20, 2017
Replies
1
Views
1K
MHB
Can You Prove the Minimum Value of a Trig Expression Given Certain Conditions?
Oct 13, 2017
Replies
1
Views
1K
MHB
What is the value of $\gamma-\alpha$ for a given $\cos$ equation?
Oct 6, 2017
Replies
1
Views
1K
MHB
Prove AB CD + AD BC < AC(AB+AD) for Convex Quadrilateral ABCD
Sep 29, 2017
Replies
1
Views
1K
MHB
What Are the Possible Values of (ab+cd)/(ad+bc)?
Sep 21, 2017
Replies
1
Views
1K
MHB
How Can You Paint 16 Seats in Consecutive Odd Red or Green Colors?
Sep 13, 2017
Replies
1
Views
1K
MHB
How to Solve This Week's POTW Quadruple Equations?
Sep 4, 2017
Replies
1
Views
1K
MHB
Quadrilateral Circumscribed Circle Diagonals and Chords Concurrency Proof
Aug 28, 2017
Replies
1
Views
1K
MHB
Can You Prove This Challenging Inequality for x Between 1.5 and 5?
Aug 21, 2017
Replies
1
Views
1K
MHB
How Do You Calculate the Integral of f(x) from 0 to e?
Aug 12, 2017
Replies
1
Views
1K
MHB
How Can You Minimize |x|-|y| Given Logarithmic Constraints?
Aug 5, 2017
Replies
1
Views
1K
MHB
Integral Sum Problem #272: Find the Integral Part of a Sum
Jul 28, 2017
Replies
1
Views
1K
MHB
How Do You Prove Equidistance in This Isosceles Right Triangle Geometry Problem?
Jul 20, 2017
Replies
1
Views
1K
MHB
What Is the Smallest k for a Cubic Function to Have Exactly One Real Root?
Jul 15, 2017
Replies
1
Views
1K
MHB
How Many Digits Are in $19^{9^9}$?
Jul 8, 2017
Replies
1
Views
1K
MHB
Can You Solve the Sum of Reciprocals for the Fourth Root Function?
Jun 29, 2017
Replies
1
Views
1K
MHB
What is the Sum of Squares in POTW #267?
Jun 22, 2017
Replies
1
Views
1K
MHB
Minimal Possible Values of Triangle Point Distances - POTW #266 Jun 7th, 2017
Jun 15, 2017
Replies
1
Views
1K
MHB
Can Rational Triples Simplify Nested Cubic Roots?
Jun 7, 2017
Replies
1
Views
1K
MHB
How Do You Calculate the Sum of Specific Binomial Coefficients?
May 29, 2017
Replies
1
Views
1K
MHB
What is the solution to this week's challenging integral problem?
May 20, 2017
Replies
1
Views
1K
MHB
Acute Triangle ABC: Proving Perpendicular Lines AD and EF
May 9, 2017
Replies
1
Views
1K
MHB
What Values of k Make the Equation Have One Non-Negative Root?
May 3, 2017
Replies
1
Views
1K
MHB
How Do You Find AC/AB Given Tan Ratios in a Triangle?
May 3, 2017
Replies
1
Views
1K
MHB
Solution for POTW #259: Finding the Value of a Trigonometric Expression
Apr 22, 2017
Replies
1
Views
1K
MHB
Can a Triangle with Sides from This Number Set Avoid Being Isosceles?
Apr 8, 2017
Replies
1
Views
1K
MHB
Is $X$ Larger Than $Y$ in POTW #257?
Mar 29, 2017
Replies
1
Views
1K
MHB
How to Solve for Triples in Equation with Absolute Value?
Mar 20, 2017
Replies
1
Views
1K
MHB
Does the Triangle's Centroid Lie Inside the Circle with Diameter OA?
Mar 13, 2017
Replies
1
Views
1K
MHB
What Is the Exact Value of the Real Root in the Equation \(x^3 + 3x - 2 = 0\)?
Mar 3, 2017
Replies
1
Views
1K
MHB
What is the Value of x in the Equation $\sqrt{x^3+1648}-\sqrt{4949-x^3}=75$?
Feb 19, 2017
Replies
1
Views
1K
MHB
How Can You Maximize This Square Root Expression for All Real Numbers?
Feb 9, 2017
Replies
1
Views
1K
MHB
What Is the Value of a+b If (a+√(a²+1))(b+√(b²+1))=1?
Feb 1, 2017
Replies
1
Views
1K
MHB
Find the Value of a Polynomial with Given Constraints - POTW #250 Jan 17th, 2017
Jan 24, 2017
Replies
1
Views
1K
MHB
What Is the Winning Probability for Player One in an N-Sided Die Game?
Jan 17, 2017
Replies
1
Views
1K
MHB
Can You Prove the Inequality in This Week's Math Challenge?
Jan 7, 2017
Replies
1
Views
1K
MHB
What is the decimal part of the sixth power of the sum of two square roots?
Jan 1, 2017
Replies
1
Views
1K
MHB
Can You Solve This Week's Math Challenge Equation?
Dec 27, 2016
Replies
1
Views
1K
MHB
Problem of the week #245 Dec 14th, 2016
Dec 20, 2016
Replies
1
Views
1K
MHB
Probability of |x-y|>=6 for Two Numbers in Range [0,10]
Dec 14, 2016
Replies
1
Views
1K
MHB
What Are the Last Two Digits of the Sum of Factorials from 7! to 2016!?
Dec 6, 2016
Replies
1
Views
1K
MHB
Can You Find a Function That Satisfies This Integral Equation?
Nov 29, 2016
Replies
2
Views
1K
MHB
Can You Solve This Complex Quadratic Expression by Hand?
Nov 21, 2016
Replies
2
Views
2K
MHB
Can xyz Exceed 1 Given x^2 + y^2 + z^2 + xyz = 4?
Nov 12, 2016
Replies
1
Views
1K
MHB
What Are the Solutions for the Exponential Equation \( x^{(y^z)} = (x^y)^z \)?
Nov 5, 2016
Replies
1
Views
1K
MHB
Can You Solve the Triangle $PQR$ Equation from POTW #238?
Oct 28, 2016
Replies
1
Views
1K
MHB
Can You Solve the Trigonometry Puzzle of the Week?
Oct 20, 2016
Replies
1
Views
1K
MHB
What is the solution to evaluating this fraction series?
Oct 11, 2016
Replies
1
Views
1K
MHB
How to Minimize the Sum of Squares with Given Distinct Elements?
Oct 5, 2016
Replies
1
Views
1K
MHB
Can You Solve the Trigonometric Equation for \(\tan^2 9^\circ\)?
Sep 27, 2016
Replies
1
Views
1K
MHB
How Many Ways to Fit Six People in Four Rooms?
Sep 20, 2016
Replies
1
Views
1K
MHB
Find the Ratio of BG to FG in a Figure with Given Side Lengths
Sep 14, 2016
Replies
1
Views
1K
MHB
How Do You Solve the Integral Challenge from POTW #231?
Sep 6, 2016
Replies
1
Views
1K
MHB
Solution for POTW #230: Calculate g^(3)(0) for f(x)
Aug 31, 2016
Replies
1
Views
1K
MHB
Can You Solve the Cube of Cosines for Specific Angles?
Aug 23, 2016
Replies
1
Views
1K
MHB
Can You Solve This Challenging Inequality Involving Real Numbers?
Aug 17, 2016
Replies
1
Views
1K
MHB
Is Sin 1 Less Than Log Base 3 of Root 7?
Aug 8, 2016
Replies
1
Views
2K
MHB
Proving the Non-Perfect Square Property of 4 Consecutive Positive Integers
Aug 1, 2016
Replies
1
Views
1K
MHB
How Can You Rewrite x²/(x⁴+x²+1) Using u?
Jul 26, 2016
Replies
1
Views
1K
MHB
Triangle Inequality Proof: Shortest Side in Relation to Sides a, b, and c
Jul 20, 2016
Replies
1
Views
1K
MHB
What are the positive integers for which $n^8+n^4+1$ is prime?
Jul 11, 2016
Replies
1
Views
1K
MHB
How Can You Express Cos(a-b) in Terms of m and n?
Jul 5, 2016
Replies
1
Views
1K
MHB
Solution from greg1313:Solution from lfdahl:
Jun 27, 2016
Replies
1
Views
1K
MHB
How Much Work to Pull Up a Second Rope on a Building?
Jun 20, 2016
Replies
1
Views
1K
MHB
Where Does \(\frac{3}{7}\) Appear for the 5th Time in the Rational Series?
Jun 14, 2016
Replies
1
Views
2K
MHB
How Many Distinct Numbers Are in This Mathematical Sequence?
Jun 7, 2016
Replies
1
Views
1K
MHB
Prove: $ab+ 2a^2b^2 \le a^2 + b^2 + ab^3$ for 0 ≤ a ≤ 1 and 0 ≤ b ≤ 1
May 31, 2016
Replies
1
Views
1K
MHB
Is the Expression Involving Inverse Squares of Differences a Square?
May 24, 2016
Replies
1
Views
1K
MHB
How Can You Determine the Values of ab+cd Given These Equations?
May 17, 2016
Replies
1
Views
1K
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MHB Math Problem of the Week
POTW High School
Welcome to the High School POTW forum!
Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one math problem each week at the advanced high school student or secondary level.
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