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Thank you all for welcoming me so heartily
I guess I can give you some hints about the solution...you can consider the fact that log is a concave function.
7+3√5 = (14+6√5) / 2 = ( 3 + √5 )² / 2
there fore , √(7+3√5) = ±(3 +√5)/√2 = (3√2 / 2) + (√10 / 2)
No mathsy thats not quite a proof...but I can give you hints if you want...this is simple...indeed
Hi to all of you and thank you for giving me such a warm welcome.
\ _  we move the first stick in the numerator

_  we place it at bottom end in the denominator
 
_ / we move the remaining stick in the numerator
 
_ we shift it in the numerator to the position where the first stick was
 
Is this ok?
For problem#K+101
It does not hold for n=2... as (2!+1)=3,which is a prime number.
Ganesh ,by infinitely many values of n , do you mean large values of n? Then what is the lower limit for n?
For the problem K+100 the answer should be 34..
(4C1*3C2)+(4C2*3C1)+(4C3*3C0)=12+18+4=34
prove that ,
u (to the power)n × v(to the power)(1n) ≤nu + (1n)v
n∈(o,1) and u,v > 0
by the way how do I bring this superscripts ? As word files are not working.
No thats not quite right I guess.Anyway the glsses cannot be stacked and should be placed seperately.
I repeat my question ....there is a point within a polygon of 10 sides , suppose ABCDEFGHIJ...take a point inside , say O.and join the vertices with this point producing 10 triangles,viz, AOB,BOC,COD,DOE,EOF,FOG,GOH,HOI,IOJ,JOA.
now you have got to select three triangles out of these 10 so that no two are adjacent.
Ganesh you are not right...there are actually less choices.
The glasses should be on a plane and therefore the idea of a tetrahedron by Maths Is Fun rules out.
Ganesh,you are trying to draw four equilateral triangles...but then does the angles agree with the theorem that they should be each 60 degrees or the totality of all the angles in a triangle should be 180 degrees?
Ricky ,I didnot quite get your point . May be the fact that I forgot to mention that the glasses should be identical can clear your confusion about the question.
Can you place four glasses on a table so that the distances of each glass from the other is exactly the same?
Here goes a simple permutation and combination puzzle..
There is a polygon with 10 sides.A point is there in the middle of the polygon and all the vertices are joined with the point and therefore producing 10 triangles.In exactly how many ways can you select three triangles no two of which are adjacent?
Hi!
I am the newest member I guess.I entered the Maths Is Fun site just 1 and 1/2 hour ago and found the logic puzzles.It was great solving the puzzles.
The answers are German owns the Fish and Hannah owns the Crocodile.
I guess the 2% idea was not correct. Is it?
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