**xizor said:****rasenshiruken973 said:**
Lol ikr he worked it out by P(Koro Sensei doesn't pick real bomb on 1st book) x P(doesn't pick real bomb on 2nd book) x P(doesn't pick real bomb on 3rd book) x P(doesn't pick real bomb on 4th book) = 4/5 x 3/4 x 2/3 x 1/2 = 1/5

instead of just finding P(principal gets real bomb on 5th book) = 1/5.

Those two types of solutions are basically what happened in that final math question with Karma and Asano. And it happens a lot in real math too, lke when after pages of calculations you notice some symmetry and solve the problem in two lines.

I understood Terasaka's process, but wondered why he went the complicated route. Ya the 5 books have uniform probability to get 1 real bomb so 1/5 for the last book (or any chosen book).

Korosensei's problem is standard trig problem, same with the one below. Not hard but take more time than that handle rising.

I liked the analogies of Asano's shots meeting in the middle idea to form the D0 domain boundary, and Karma's on vertices like classmates with unique talents, with only 1/8 visible to his own cube. I get Asano's way (requires lots of volume calculations). Karma's seems simple, I got the symmetry 1:1 idea, but not the sphere thing.

Asano's diagram is a truncated octahedron (8 hexagons, 6 squares, all edges length A).

https://en.wikipedia.org/wiki/Truncated_octahedron
If Karma replaced the sphere with the correct shape above, then including the outsides cubes, dividing to 8 portions, noticing the symmetry makes sense.

I had a third way similar to Karma. Only consider 1 cube, divide into 8 equal cubes. Each subcube cut thru the octahedron, would yield 2 symmetric pieces, with each piece volume v=(0.5a)^3/2. Octahedron has 8 pieces, so V = (0.5a)^3/2*8 = 0.5a^3.

If they studied crazy like their school, they probably memorized properties of solids. So octahedron volume formula:

V = 8*sqrt(2) * A^3

A is edge length, but problem gives a=1=cube side length. After some triangle identities etc I have this conversion:

A = a/4*sqrt(2)

Messy stuff:

V = a^3 * 2^(3.0/2) * 2^0.5 * 8./ 4^3

V = a^3 * 0.5

So that's the fourth way. Anyways it was fun. Btw all teachers I've seen mark at most half marks if we had the answer without derivation, like what Karma did it seems. Some required we write verbose paragraphs to explain reasoning & proof steps.