Math Is Fun Forum

I did suspect once that PowerOfPi at AoPS was the same as LuisRodg over here because they had the same avatar; now I’m not so sure.

2) Hint: Does

I’m getting a picture of probability density function in quantum mechanics here.

To elaborate, the condition that no four (or fewer) teachers know all the answers means that if

Thanks Avon! You’re a genius.

Well, unless I see a counterexample, I will stick to 210 as the answer.

Here is a smaller example to illustrate my point.

Teacher 1: {1,2,3,4,5,6}
Teacher 2: {1,2,3,7,8,9}
Teacher 3: {1,4,5,7,8,10}
Teacher 4: {2,4,6,7,9,10}
Teacher 5: {3,5,6,8,9,10}

Thus no two teachers have the complete set but any three teachers do. Again 10 may not be the minimum answer, but, as you can see for yourself, it works.

The way I do it is to solve the differential equation (by separating the variables and integrating) getting the general solution

Or your route could be like this:

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In which case the IVT applies but Rolle’s theorem does not!

This is a very important result indeed. As Bertrand Russell and Alfred North Whitehead showed in their magnum opus Principia Mathematica, it is necessary to prove that 1 + 1 = 2 in order to “re-invent mathematics with set theory”.

[align=center]http://www.youtube.com/watch?v=BE657F9sqyQ[/align]

I also thrashed the computer at Othello! Look!

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HAHAHAHAHA!!!!

Thanks! Fixed.

The point is that if your number is an odd multiple of 5, step 3 will produce a number ending in 24, while if your original number is a multiple of 10, step 3 will produce a number ending in 99. I forgot about the latter.

Hence, if n is the number of 1’s,

Now

Thus

Hence we have the required formula

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