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Challenge Questions and Puzzles

Have a challenging question or puzzle you want to share with the community? Post it here (homework questions do NOT belong here).
ranga519
Challenge. Difficulty level - medium
Replies
0
Views
460
ranga519
ranga519
W
Square in triangle...
Replies
6
Views
866
Monoxdifly
Monoxdifly
W
Weird puzzle
Replies
0
Views
467
Wilmer
W
lfdahl
Limit of the smallest function value
Replies
1
Views
498
lfdahl
lfdahl
W
Sticky spitballs
Replies
3
Views
625
Wilmer
W
lfdahl
Probability Challenge
Replies
2
Views
524
lfdahl
lfdahl
lfdahl
Prove the inequality (a^3-c^3)/3≥abc((a-b)/c+(b-c)/a)
Replies
3
Views
601
lfdahl
lfdahl
lfdahl
Smallest sum of fractions
Replies
2
Views
531
lfdahl
lfdahl
lfdahl
Evaluate the product ∏(1+10^(-2^n))
Replies
2
Views
490
lfdahl
lfdahl
lfdahl
Find with proof the integer
Replies
2
Views
1K
lfdahl
lfdahl
lfdahl
Prove the binomial identity ∑(-1)^j(n choose j)=0
Replies
3
Views
1K
lfdahl
lfdahl
anemone
[SOLVED] Inequality involves radical, square and factorial expression 3!√{x}+2!y+1!z^2⩽ 13
Replies
6
Views
831
kaliprasad
kaliprasad
J
Integration ∫ [√(sin^2 x-3sin x+2))/√(sin^2 x+3sin x+2))]dx
Replies
1
Views
525
jacks
J
lfdahl
A positive integer divisible by 2019 the sum of whose decimal digits is 2019.
Replies
2
Views
628
lfdahl
lfdahl
lfdahl
Determine all real x in x^n+x^(-n)
Replies
5
Views
620
lfdahl
lfdahl
lfdahl
Evaluate the double sum of a product
Replies
2
Views
758
lfdahl
lfdahl
J
ordered pair (x,y): x choose y = 2020
Replies
2
Views
648
jacks
J
J
⌊ 2020!/(1!+2!+3!+..+2019!)⌋
Replies
2
Views
673
jacks
J
J
Evaluate ⌊ 1/a_1+1/a_2+...+1/a_{2008} ⌋
Replies
2
Views
563
jacks
J
J
Binomial Sum \displaystyle \sum^{n}_{k=0}\binom{n+k}{k}\cdot \frac{1}{2^k}
Replies
1
Views
826
jacks
J
Olinguito
Challenge Problem #6: Prove tan 18°=√(1-2/√5)
Replies
3
Views
636
Olinguito
Olinguito
anemone
Unsolved Challenge Challenge question on equilateral triangle: Prove ∠DBA=42°
Replies
5
Views
737
Wilmer
W
anemone
Unsolved Challenge Solving equation in natural number
Replies
1
Views
616
topsquark
topsquark
E
Cardinalities of finite sets
Replies
2
Views
710
Country Boy
C
T
Unsolved Challenge A tough Integral
Replies
9
Views
2K
MountEvariste
MountEvariste
J
Sum of two infinite series: Σ[1/(36r^2-1)+2/(36r^2-1)^2]
Replies
2
Views
894
jacks
J
lfdahl
Inequality - solve in at least two ways
Replies
8
Views
1K
lfdahl
lfdahl
W
Don't you be no square!
Replies
8
Views
959
Klaas van Aarsen
Klaas van Aarsen
W
ANUTter puzzle...
Replies
5
Views
747
Wilmer
W
lfdahl
Infinite sum: Evaluate (2x-1)/(1-x+x^2)+(4x^3-2x)/(1-x^2+x^4)+(8x^7-4x^3)/(1-x^4+x^8)
Replies
6
Views
1K
lfdahl
lfdahl
anemone
Solved Challenge Trigonometric inequality: sin (1/(n+1934))<1/1994
Replies
3
Views
761
castor28
castor28
L
EASY Mathmatical Puzzle
Replies
3
Views
784
Monoxdifly
Monoxdifly
MountEvariste
Volume in R4
Replies
1
Views
780
MountEvariste
MountEvariste
S
set theory
Replies
5
Views
1K
MarkFL
M
lfdahl
Prove the inequality
Replies
6
Views
1K
lfdahl
lfdahl
anemone
Solved Challenge System of Equation Challenge (a+b)(b+c)=-1
Replies
3
Views
919
topsquark
topsquark
lfdahl
Is the definite integral ∫ [arcsin(1/x)-1/x]of indeterminate form?
Replies
2
Views
692
lfdahl
lfdahl
lfdahl
Find the smallest possible value 1-1/(n_1)-1/(n_2)-1/(n_3)
Replies
4
Views
750
lfdahl
lfdahl
anemone
Solved Challenge Find the sum of a^(1/3)+b^(1/3)+c^(1/3)
Replies
2
Views
841
anemone
anemone
T
Unsolved Challenge Simple closed form for integral
Replies
3
Views
1K
lfdahl
lfdahl
T
Tricky Logic Puzzle with 26 Variables
Replies
3
Views
820
Wilmer
W
anemone
Which of the two logarithms is larger: log_7 (10) or log_11 (13)
Replies
6
Views
1K
kaliprasad
kaliprasad
W
Bingo!
Replies
0
Views
525
Wilmer
W
Olinguito
Challenge problem #5 [Olinguito]
Replies
2
Views
704
Olinguito
Olinguito
F
Tricky Question (for which I do not know the answer)
Replies
0
Views
566
fb3342
F
mrtwhs
Thumbtacks
Replies
1
Views
560
mrtwhs
mrtwhs
S
Propositional calculus
Replies
10
Views
2K
solakis
S
MountEvariste
Prove that the maximum number of mutually commuting linearly independent complex matrices of order n is equal to ⌊n^2/4⌋+1
Replies
2
Views
913
MountEvariste
MountEvariste
MountEvariste
A Hankel Determinant Limit
Replies
2
Views
908
MountEvariste
MountEvariste
Olinguito
Challenge problem #4 Is it possible for all n switches to be on at the end
Replies
2
Views
745
Olinguito
Olinguito
Olinguito
Challenge problem Find k if x=k is tangent to the curve y=x+√(2).e^[(x+y)/√(2)]
Replies
4
Views
918
solakis
S
S
axiomatics
Replies
16
Views
2K
steenis
S
mrtwhs
Circumcircles Find a formula relating R,R_1,R_2.
Replies
2
Views
796
mrtwhs
mrtwhs
Olinguito
Challenge problem #2 Show that 5φ^2n+4(−1)^n is a perfect square
Replies
3
Views
689
Olinguito
Olinguito
W
Loan @ 3 rates
Replies
8
Views
979
Wilmer
W
T
Tanh Integral
Replies
1
Views
578
Greg
Greg
T
Unsolved Challenge Integral of tan, ln
Replies
0
Views
377
Tony
T
T
Unsolved Challenge An interesting Integral = (2π)^2(ln2)
Replies
0
Views
428
Tony
T
T
Unsolved Challenge Five, Phi and Pi in one integral = −5ϕπ
Replies
3
Views
789
Tony
T
T
Unsolved Challenge Long Integral equals (π/2)^2−[2ln(2)/]π^2+ln^2(2)/(2π)
Replies
0
Views
374
Tony
T
T
Unsolved Challenge Integral of sine = 27/2+ln^2(2)+ln(2)
Replies
3
Views
605
Tony
T
T
Unsolved Challenge Integral of product = π/9[12ln(2)−1]
Replies
0
Views
402
Tony
T
Olinguito
Challenge problem #1 Solve 2x^2y^2−2xy+x^2+y^2−2x−2y+3=0
Replies
4
Views
646
Olinguito
Olinguito
T
Unsolved Challenge imaginary integral = π/(1+n)
Replies
1
Views
429
Opalg
Opalg
T
Unsolved Challenge arctan integral = π^2/20
Replies
0
Views
387
Tony
T
T
Unsolved Challenge Quite complicated integral= sin(π/12)
Replies
0
Views
315
Tony
T
T
Unsolved Challenge Result Integral = ln2−ζ(2)/4
Replies
0
Views
344
Tony
T
lfdahl
Fish pond challenge: show that it tends to an equilibrium amount between x_0/2 and x_0.
Replies
3
Views
639
lfdahl
lfdahl
Theia
Maximum Displacement in Projectile Motion: show that angle between initial velocity vector and velocity vector at time T is π/2
Replies
2
Views
599
Theia
Theia
T
Unsolved Challenge A hard integral gives a simple closed form, π/(4a)^3
Replies
1
Views
483
GJA
G
T
Unsolved Challenge Oloa Olivier's type integral π/4
Replies
0
Views
452
Tony
T
lfdahl
Trigonometric product challenge
Replies
2
Views
553
topsquark
topsquark
Klaas van Aarsen
Escape from the velociraptor
Replies
5
Views
1K
Klaas van Aarsen
Klaas van Aarsen
lfdahl
Evaluate the definite integral x/√(e^x+(2+x)^2)
Replies
1
Views
567
lfdahl
lfdahl
T
Unsolved Challenge Mathematical puzzle What is the possible number of ways Lucy can fill an Odiosis board
Replies
1
Views
622
castor28
castor28
lfdahl
A center of mass determined triangle: Find the angles of the triangle P_1P_2P_3
Replies
1
Views
607
lfdahl
lfdahl
lfdahl
Solve the equation cos^8θ+sin^8θ−2(1−cos^2θsin^2θ)^2+1=0
Replies
4
Views
826
lfdahl
lfdahl
lfdahl
Determine the functions
Replies
2
Views
686
lfdahl
lfdahl
lfdahl
Polynomial congruence
Replies
2
Views
614
lfdahl
lfdahl
lfdahl
What is the largest possible area of a simple quadrilateral, two sides of which have length a and two sides of which have length b?
Replies
4
Views
1K
lfdahl
lfdahl
M
Find the ACB angle if the orthocenter of this triangle belongs to the circumscribed circle of the triangle AOB
Replies
0
Views
490
maxkor
M
Klaas van Aarsen
Divide into 2 congruent pieces
Replies
2
Views
773
Klaas van Aarsen
Klaas van Aarsen
lfdahl
Find the infinite sum of fractions 2/(3⋅5)+(2⋅4)/(3⋅5⋅7)+(2⋅4⋅6)/(3⋅5⋅7⋅9)+...
Replies
8
Views
2K
lfdahl
lfdahl
Klaas van Aarsen
Divide into 5 congruent pieces
Replies
2
Views
642
Klaas van Aarsen
Klaas van Aarsen
lfdahl
Prove the lim n→∞ (1^1+2^2+3^3+...+(n−1)^(n−1)+n^n)/(n^n)=1.
Replies
3
Views
799
MountEvariste
MountEvariste
lfdahl
Find the antiderivative of V(2−x−x^2)/x^2
Replies
2
Views
620
Opalg
Opalg
anemone
Solved Challenge Solve for θ
Replies
1
Views
554
Klaas van Aarsen
Klaas van Aarsen
kaliprasad
Show that sin10∘ is irrational number
Replies
8
Views
1K
Greg
Greg
lfdahl
Evaluate the product of sines: sin1sin2sin3…sin89
Replies
5
Views
1K
lfdahl
lfdahl
lfdahl
n is a good number, if in any subset of M of size n there are two elements a and b such that a+b is a prime number
Replies
2
Views
687
lfdahl
lfdahl
lfdahl
What is the probability that there is a point Q in T whose distance from P is larger than the altitude of T?
Replies
1
Views
602
lfdahl
lfdahl
lfdahl
Sum to product inequalities
Replies
5
Views
1K
lfdahl
lfdahl
lfdahl
Root function inequality
Replies
4
Views
1K
lfdahl
lfdahl
lfdahl
Integral challenge ∫ln2(1+x^(−1))dx
Replies
4
Views
1K
lfdahl
lfdahl
lfdahl
Find the exact sum of the series 1/(1⋅2⋅3⋅4)+1/(5⋅6⋅7⋅8)+...
Replies
5
Views
927
MountEvariste
MountEvariste
castor28
Weird function challenge: Exhibit a function from R to R such that the image of any open interval is the whole of R.
Replies
12
Views
2K
castor28
castor28
lfdahl
Dice rolling -Which of 2,6,1006 is more likely to be one of these totals?
Replies
8
Views
1K
lfdahl
lfdahl
lfdahl
Determine the integer n if the decimal digits of n are reversed to obtain N, then N−n=999s
Replies
7
Views
1K
lfdahl
lfdahl
castor28
Liars and truthtellers: What is the minimum number of yes-no questions he must ask the inhabitants in order to find the 5 knaves?
Replies
1
Views
546
castor28
castor28
lfdahl
Determine the number of integers for which the congruence is true
Replies
2
Views
833
lfdahl
lfdahl
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