lets see your solutions for this

>>7913892
20. An n+1 dimensional tetrahedron looks, on layer 4, like an n-dimensional tetrahedron.

>>7913898
/thread

too bad, first reply is correct :D

brb, preparing further question

>>7913898
Yep
This isn't even hard OP you gave us the solution

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>>7913901
The total number of balls in the 4d tetrahedron with n layers can have a closed form.

>>7913912
Nice one there.

>>7913919
thanks I got too lazy to simplify but it should be a cubic polynomial. the 4d case will be a quartic polynomial

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ok

heres the new one :)

>>7913980
you are telling to wrong.
a point where someone does not know their hat gives information. WIthout some form of time this doesn't work.

>>7914026
indicated in text imo

>>7913912
Nice, there is indeed a closed form as long as you know the closed form of the 1D case: (n+1)n/2

>>7913892
I think it's 35

In general, the number of balls in an [math]n[/math]-tetrahedron with [math]m[/math] layers is [math]\binom{n+m-1}{n}[/math]. Since the number of balls in each layer is itself the sum of the first few terms in the previous dimension's sequence, you're just repeatedly applying the hockey stick identity, so we naturally get a binomial coefficient for our answer.

>>7913980

#1 sees a green and a blue card and therefore doesnt know which card he has ==> doesnt yel

#3 sees nothing ==> doesnt yell
#4 sees nothing ==> doesnt yell
#2 knows that #1 didnt yell ==> therefore #2 (himself) and #3 cannot possibly have the same color ==> therefore he knows he has the blue card

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nice.

next one if unknown

>>7914034
it isn't

>>7914208
That doesn't work. Even if their age in years is the same, one is still younger by minutes at least.

>>7914208
x*y*z = 36
x+y+z <= 31
x < y, x < z.
x > 0, y > 0, z > 0.

Solutions:
1,4,9
1,6,6 (But this solution is unlikelly unless he had a mistress)
2,3,6

The possible dates would be 11, 13, or 14.

>>7914235
This is the first time I've seen someone who was too autistically hung up over technicalities to solve a *math problem*.

>>7914208
Only way this is possible is if he knows the age of the red-haired kid in advance

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Has anybody got that one interview question with the dates? The one somebody modified to extreme autismal levels?

>>7914253
The reason he gives you that is because, otherwise, you may think that the two youngest kids are the same age, which is a valid solution:
2,2,9 and
3,3,4

>>7914243
>>7914261
You're also missing (1,3,12) and (1,2,18). And you're forgetting that Ivan knows what day it is when he says he still doesn't know the ages of the boys. So you have to find the triples with the same sums, which are (1,6,6) and (2,2,9). So the answer is (1,6,6).

>>7914267
You are right, I in fact missed a couple solutions. So, yeah, (1,6,6) and the day is 13th

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ok, great.

thinking about what is next reasonable riddle,
btw feel free to contribute

>>7914247
When it doesn't work, it doesn't work. Not taken technicalities into account is how math errors are made.

>>7914283
truncated # of circumnavigations around sun expressed by slightly dynamic approximation of mankind

so its both

next one is something passably difficult for specialists

your starting point: dU = TdS - pdV (includes 1st + 2nd fund. theor.)(U:intrinsic energy, S:entropy, T,p,V:temperature,pressure,volume)
in addition: in view on a closed system for exchange of matter

derive the connections of the thermic state variables (p,T,V) for an adiabatic and reversible process with ideal gas