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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).
anemone
[SOLVED] Cubic Polynomial
Replies
3
Views
165
kaliprasad
kaliprasad
anemone
Solved Challenge Cyclic Quadrilateral
Replies
1
Views
177
Opalg
Opalg
anemone
[SOLVED] Evaluate trigonometric sum
Replies
1
Views
189
kaliprasad
kaliprasad
anemone
[SOLVED] Trigonometric challenge
Replies
1
Views
184
anemone
anemone
anemone
[SOLVED] Square number challenge
Replies
2
Views
237
kaliprasad
kaliprasad
anemone
Unsolved Challenge Area of triangle
Replies
0
Views
212
anemone
anemone
anemone
[SOLVED] Inequality involving a, b, c and d
Replies
1
Views
206
anemone
anemone
anemone
[SOLVED] Integral of trigonometric function
Replies
1
Views
203
Opalg
Opalg
anemone
[SOLVED] Integral challenge
Replies
2
Views
220
MountEvariste
MountEvariste
MountEvariste
A tale of two integrals
Replies
3
Views
227
MountEvariste
MountEvariste
S
System of equalities 3
Replies
6
Views
434
Monoxdifly
Monoxdifly
anemone
[SOLVED] Triangle sides challenge
Replies
2
Views
204
Opalg
Opalg
anemone
[SOLVED] Find the square of the distance
Replies
1
Views
227
Opalg
Opalg
anemone
[SOLVED] Find f(84)
Replies
4
Views
273
kaliprasad
kaliprasad
anemone
[SOLVED] Find d - b
Replies
1
Views
179
kaliprasad
kaliprasad
anemone
[SOLVED] Largest even integer
Replies
2
Views
189
Opalg
Opalg
anemone
[SOLVED] Find |k|
Replies
4
Views
246
kaliprasad
kaliprasad
anemone
[SOLVED] Floor function
Replies
3
Views
219
anemone
anemone
anemone
[SOLVED] Heptagon Challenge
Replies
1
Views
176
anemone
anemone
anemone
[SOLVED] Prove ABC is an equilateral triangle
Replies
1
Views
171
anemone
anemone
anemone
[SOLVED] Determine positive integers
Replies
1
Views
213
anemone
anemone
anemone
[SOLVED] Find a and b
Replies
4
Views
234
anemone
anemone
anemone
Unsolved Challenge Prove ∠PAB = ∠CAQ
Replies
0
Views
264
anemone
anemone
anemone
[SOLVED] Find the area of the red region
Replies
2
Views
255
anemone
anemone
anemone
[SOLVED] Show that K≥1
Replies
1
Views
319
Opalg
Opalg
anemone
[SOLVED] Find (x₁²+1)(x₂²+1)(x₃²+1)(x₄²+1)
Replies
2
Views
361
anemone
anemone
anemone
[SOLVED] Find AC
Replies
1
Views
230
anemone
anemone
anemone
[SOLVED] Find maximum b
Replies
2
Views
256
anemone
anemone
anemone
[SOLVED] Polynomial challenge
Replies
1
Views
205
anemone
anemone
S
system of equalities
Replies
2
Views
183
solakis
S
anemone
[SOLVED] Geometry challenge
Replies
3
Views
194
anemone
anemone
anemone
[SOLVED] Lengths of the sides of quadrilateral
Replies
1
Views
177
Opalg
Opalg
anemone
[SOLVED] Prove 1/3≤u/v≤1/2
Replies
4
Views
313
Opalg
Opalg
S
System of inequalities
Replies
8
Views
280
solakis
S
S
system of equalities
Replies
7
Views
203
topsquark
topsquark
anemone
[SOLVED] System of equations
Replies
1
Views
192
anemone
anemone
anemone
Unsolved Challenge cos(π/7)
Replies
0
Views
261
anemone
anemone
anemone
Solved Challenge Isosceles Triangle Challenge
Replies
2
Views
258
anemone
anemone
S
Set theory
Replies
0
Views
140
solakis
S
Opalg
Tough inequality challenge
Replies
2
Views
243
Opalg
Opalg
anemone
[SOLVED] Find b(a+c)
Replies
1
Views
195
kaliprasad
kaliprasad
anemone
[SOLVED] Inequality challenge
Replies
1
Views
179
topsquark
topsquark
anemone
[SOLVED] Find (a+b)³+(b+c)³+(c+a)³
Replies
2
Views
298
kaliprasad
kaliprasad
anemone
Prove π^e>5^(1.9)
Replies
2
Views
288
anemone
anemone
anemone
Solved Challenge Unsolved Challenge: Natural logarithm and Exponent
Replies
1
Views
165
Opalg
Opalg
anemone
[SOLVED] Evaluate the constant in polynomial function
Replies
7
Views
291
kaliprasad
kaliprasad
anemone
[SOLVED] Find the last digit of a series
Replies
2
Views
221
kaliprasad
kaliprasad
anemone
Unsolved Challenge Unsolved Challenge: Floor function
Replies
4
Views
277
topsquark
topsquark
anemone
[SOLVED] Factorials and Exponent Challenge
Replies
2
Views
235
kaliprasad
kaliprasad
anemone
[SOLVED] Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
Replies
1
Views
240
Opalg
Opalg
anemone
[SOLVED] Find |f(0)|
Replies
1
Views
238
kaliprasad
kaliprasad
anemone
[SOLVED] Prove ∠ABP=∠ACP
Replies
4
Views
218
anemone
anemone
anemone
[SOLVED] Find a, b, c and d
Replies
2
Views
241
anemone
anemone
anemone
[SOLVED] Find real solutions to a system
Replies
6
Views
209
anemone
anemone
anemone
Unsolved Challenge Unsolved Challenge: Σ(cosAcosB)>√(cosAcosBcosC)
Replies
0
Views
262
anemone
anemone
anemone
[SOLVED] Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911
Replies
3
Views
282
kaliprasad
kaliprasad
anemone
[SOLVED] A quite delicious inequality problem
Replies
1
Views
243
kaliprasad
kaliprasad
anemone
[SOLVED] Maximize 2sinxcosx/[(1+sinx)(1+cosx)]
Replies
2
Views
257
anemone
anemone
anemone
[SOLVED] Evaluate (a+c)(b+c)(a-d)(b-d)
Replies
6
Views
338
anemone
anemone
anemone
[SOLVED] Solve x³+3xy²=-49 and x²-8xy+y²=8y-17x
Replies
13
Views
436
kaliprasad
kaliprasad
anemone
Unsolved Challenge Unsolved Challenge: Trigonometric Identity
Replies
0
Views
137
anemone
anemone
anemone
[SOLVED] Prove that △ABC is isosceles.
Replies
1
Views
183
anemone
anemone
anemone
[SOLVED] Prove 1/(log₂π)+1/(log₅π)>2
Replies
1
Views
167
kaliprasad
kaliprasad
anemone
[SOLVED] Show that |q|>64
Replies
1
Views
180
Opalg
Opalg
anemone
[SOLVED] Condition for A Quartic Equation to have a Real Root
Replies
2
Views
235
anemone
anemone
anemone
Solved Challenge Find $\angle ADC$
Replies
5
Views
385
anemone
anemone
anemone
[SOLVED] Length of Shortest Side In a Triangle
Replies
6
Views
322
MarkFL
M
M
Solved Challenge Social distancing problem
Replies
4
Views
314
MarkFL
M
anemone
Integers and Divisibility Challenge
Replies
1
Views
249
anemone
anemone
Opalg
Numbers with a quadratic property
Replies
3
Views
533
Opalg
Opalg
anemone
[SOLVED] x-coordinates of Optimization Points for Polynomial Function: f(x)=(x-1)^4+(x-2)^4+...+(x-n)^4
Replies
1
Views
196
castor28
castor28
anemone
Solved Challenge Roots of a Polynomial Function A²+B²+18C>0
Replies
4
Views
468
anemone
anemone
anemone
[SOLVED] Inequality of cubic and exponential functions
Replies
1
Views
375
kaliprasad
kaliprasad
J
value of k in definite Integration
Replies
0
Views
630
jacks
J
lfdahl
Definite Integral Challenge
Replies
6
Views
2K
MountEvariste
MountEvariste
MountEvariste
Number theory problem #1
Replies
1
Views
865
Opalg
Opalg
Dhamnekar Winod
Can we apply here logic?
Replies
1
Views
892
Dhamnekar Winod
Dhamnekar Winod
J
Exponential series limit
Replies
3
Views
1K
Klaas van Aarsen
Klaas van Aarsen
J
limit
Replies
7
Views
1K
jacks
J
J
Limit with Integration
Replies
1
Views
1K
jacks
J
S
inequality
Replies
7
Views
2K
solakis
S
S
axiomatics
Replies
0
Views
994
solakis
S
S
Geometrical problem
Replies
1
Views
1K
solakis
S
S
logic problem
Replies
3
Views
1K
solakis
S
S
high school inequality |(√(sinx)+1)^2−(√(sina)+1)^2|<b
Replies
4
Views
2K
solakis
S
S
high school inequality 2 |x^2y-a^2b|<A
Replies
1
Views
653
Opalg
Opalg
S
Quadrilateral Divider
Replies
4
Views
993
Satya
S
Klaas van Aarsen
Multiple consists of only 6's and 7's
Replies
11
Views
2K
Satya
S
Klaas van Aarsen
Multiple consists of only 1's
Replies
4
Views
829
Klaas van Aarsen
Klaas van Aarsen
lfdahl
Trigonometric Sum Challenge Σtan^(-1)(1/(n^2+n+1)=π/2
Replies
3
Views
993
lfdahl
lfdahl
lfdahl
Volume of the solid obtained by rotating R around the line y=x
Replies
2
Views
701
lfdahl
lfdahl
lfdahl
Maximize the sum of squared distances
Replies
1
Views
499
lfdahl
lfdahl
lfdahl
Probability challenge Prove that the probability there is only one winner is at least 2/3
Replies
4
Views
831
steep
S
lfdahl
Find the possible values of k: x+1/y=y+1/z=z+1/x=k
Replies
2
Views
772
lfdahl
lfdahl
lfdahl
Determine all possible values a/(a+b+d)+b/(a+b+c)+c/(b+c+d)+d/(a+c+d)
Replies
2
Views
770
lfdahl
lfdahl
lfdahl
Limit of integral challenge of (e^(-x)cosx)/(1/n+nx^2)
Replies
2
Views
684
lfdahl
lfdahl
L
Static Analysis of Truss
Replies
0
Views
463
littlemac
L
L
Electrical Engineering Problem
Replies
1
Views
512
skeeter
skeeter
S
Constractive dilemma
Replies
1
Views
707
solakis
S
Olinguito
Unsolved Challenge Challenge Problem #7: Σ(x/(y^3+2))≥1
Replies
2
Views
894
topsquark
topsquark
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