hehe, my try:-

fire up your will to smoke, use this fire to light the cigar.

does this work?

i think

a bull attacked her ???

1 think puzzles me that if he had 6 sausages and the no. of family members are 5, then does he plan to invite just 1 guest.

if yes, then 13 guests+ 5 members of family = 18 = 3 packets, so ans shud be 0. and yeah , keep making more riddles but make them tougher

i think i got it

traffic lights??

just guessing....

a crow?

dictionary

use spoilers plz.

it will be a multiple of l.c.m. of 1,2,3,4,5 and 6 and then add 1

61,121,181,241 dont work burt 301 does

edit : typo

Some sweet, some strange, some true messages

1. The worst think we can regret is not for the things that we did wrong, but for the things that we could have done right but never did.

2. Life is very funny. Something you love the most can turn into something you hate the most. For example, set your favorite song as alarm tone.

3. Trust the one who can see three things in you: sorrow behind your smile, love behind your anger and reason behind your silence.

4. If you do regular studies, it means that you don't have enough confidence. Study at the last moment and show your confidence.

5. If we use quadratic formula and keep it equivalent to 0, then take the square root of of the variable, then differentiate the answer and put the final answer in the given equation, neglect the constant and plot the graph of its inverse, then can we................

make a paper plane from that graph paper

6. The shortest distance between two people is not a straight line but a curve - a smile. The more you bend this curve, the shorter the distance gets.

7. Fact of today: old people drive like they have all the time in the world, but younger generation drives as though their days are limited.

8. Best message forever in the galaxy - Do you know why love is blind? Love is blind because your mom started to love you even before seeing your face.

9. Brilliant doubt but unanswered - How come Price and Worth have same meaning but, priceless and worthless are opposites.

10. Funny but true - Combined study is meeting with friends where all aspects of the world will be discussed except studies.

All were them were so true, but for me the 1st was the BIGGEST TRUTH

this works!!

however another go:-

If n + 3 and n2 + 3 are both perfect cubes then their product must also be a perfect cube.

So consider (n + 3)(n² + 3) = n³ + 3n² + 3n + 9 = (n + 1)³3 + 8.

This can be a perfect cube only if it is 8 more than another perfect cube, namely (n + 1)3.

The only pairs of perfect cubes that differ by 8 are (−8, 0) and (0, 8).

So we must have

(n + 1)³ = (−2)³ n = −3; or

(n + 1)³ = 0³ n = −1.

For neither of these solutions is n2 + 3 a perfect cube.

Therefore, if n is an integer, n + 3 and n2 + 3 cannot both be perfect cubes.

correct again!!

The general equation for 3³+4³+5³ = 6³ is [k^1/3×3]³+ [k^1/3×4]³+[k^1/3×5]³ = [k^1/3×6]³. Thus, besides 3³+ 4³+5³ = 6³ for k=1, there is 6³+8³+10³ = 12³ for k=2, 9³+12³+15³ = 18³ for k=3, etc.

In addition, there is the general equation [k^1/3×11]³+[k^1/3×12]³+[k^1/3×13]³+[k^1/3×14]³ = [k^1/3×20]³ for 11³+12³+13³+14³ = 20³ for k=1, 22³+24³+26³+28³ = 40³ for k=2, 33³+36³+39³+42³ = 60³ for k=3, etc.

i am giving u a prize

There are two definitions to a perfect cube (and perfect square). First is where the cube (or respectively, square) root must be an integer, and second where it does not need be an integer, but must be a rational number. I shall assume here the more limited definition that a perfect cube must be an integer.

(n² + 3) - (n + 3) = (n - 1)n

The difference between two cubes can be expressed as:

a³ - b³ = (a - b)(a + b)²

Let n = (a + b)², then by subsitution:

(a - b) = (a + b)² - 1

The equation can be formed as the quadratic:

a² + (2b - 1)a + (b² + b - 1) = 0.

The discriminant Δ of the quadratic is -8b + 5.

From the nature of the discriminant, for the polynomial to have at least one real root, i.e. Δ >= 0,

b <= 5/8.

In order for b³ to be a perfect cube _{(see definition above)}, b must be an integer < 5/8, and in order for a to be an integer

-8b + 5 must be a perfect square of an integer: x² = -8b + 5.

Let b = kx to form the quadratic equation: x^2 + 8kx - 5 = 0.

(x + i√5)² = x² + 2i√5 - 5, thus, in order for the quadratic equation to be a perfect square 8k = 2i√5, i.e., k = i√5/4. Substituting k = i√5/4 into the quadratic gives: x² + 2i√5x - 5 = 0. Solving for the roots of x, gives x = -i√5. Substituting this value back into x² = -8b + 5 gives b = 5/4, which is neither an integer nor would b be < 5/8. Ergo both (n² + 3) and (n + 3) can not be perfect cubes.

sorry for me being lazy to not read the complete soln but

a³ - b³ = (a - b)(a ²+ b² +ab)

and not what you wrote

Okay then ----

6^3+8^3+10^3=12^3

9^3+12^3+20^3=18^3

12^3+16^3+20^3=24^3

15^3+20^3+25^3=30^3

18^3+24^3+30^3=36^3

That should be enough to find a distinct pattern

Sorry for being lazy and not using superscript.

1st is correct,

2nd shud have 15 cube (too lazy)

3rd ok,

4th ok,

5th ok,

yes i observe the pattern thanks a lot

If A and B are running in a circular track in a direction opposite to that in which C is running who, infact is running at twice and thrice the speed of A and B respectively and on the same track they start running from the same point. It is known that A's average speed is 3m/sec and track is 120m in length. When will B, after start find himself equidistant between A and C for the first time??

well 120/7 seconds is the 2nd time, the 1st time is after 120/9 seconds as A and C will meet after 120/9 seconds and B wud be behind A, equidistant from A and C.

crumple "b" into a ball then crumple "a" around it, ensuring "a" would always land first.

thats what i thought too but then B will never land , i guess

there are two sheet of paper (paper sheet A and paper sheet B)of equal size(height, length, width ) and weight and drop them from same height then how would you ensure that paper sheet A would land first??(Of course, nothing could be attached and added to either sheet of paper.)

good luck..

by folding paper A as much as we can so that it rips through air and land faster ( this wud work in non vacuum medium)

n+3 is a red herring! n^2+3 can never be a perfect cube.

wherez d proof? smart though!

I put your premise into a spreadsheet

I stopped at 32727 and found no occurrence where three consecutive numbers cubed totaled to a perfect cube, which is what I expected..

thats ok, but why take consecutive numbers only? i said AP with a common diff. d , not d=1

i recently came across this:-

3³+4³+5³=6³

i am curious to know if there are more of this kind i.e. sum of cubes of nos. in arithmetic progression = to cube of some other no.

Let x be the cube root of n+3 and y be the cube root of n^2+3.

I used spreadsheet to solve for n and y for all x from -50 to 50. There were no integral y solutions. There is an interesting pattern. For all absolute x greater than 6, y = x^2-2/x. For x between -6 and 6, this approximation is less accurate but is pretty exact for all other x. And for any x greater than 2, the term 2/x will always be less than 1 so for integral x, y will always have a fraction or decimal. As x approaches infinity, this decimal approaches zero and y approaches x^2. y=x^2 is what would be the case if x were simply cube root of n and y cube root of n^2 as well, the addition of the 3 in both equations just throws it off a bit, but for larger and larger n that matters less and less and y gets closer and closer to x^2, but never quite reaches it, thus it will always be a non-integer.

yes u r right, but i asked for a mathematical reasoning, not using spreadsheets, no offence though

By definition of a perfect cube, (n² + 3) and (n + 3) must be integers, and so then must be their difference. The difference between (n² + 3) - (n + 3) is n(n - 1).

The factors of n(n-1) are n and n-1. The only primes that have a difference of 1 is 3 and 2, thus for n to be an integer in the expression n(n-1), n must equal 3. Neither [3]+3 = 6 nor [3]^2+3 = 12 are perfect cubes.

Ergo, both (n² + 3) and (n + 3) can not be perfect cubes.

is it really true that the difference between 2 perfect squares equal to the product of 2 prime nos??

perfect cube not perfect square wolfgang , and reasoning also needed. now i am off to sleep. see ya tmrw

sure that marine slapped the officer, but who kissed the girl then??

and hints are also available when u ask.