Solution to Homura's Math Problem

In episode 10 of Madoka Magica Homura is presented with a math problem she can't solve. Poor Homura, she has been in bed for the last 6 months and as soon as she goes back to school she has to face this!

Let's help her!
Homura-chan, the next time you go back in time, please check this before going to school!

This is Homura's problem:

and this is the solution:

Immediately before her problem, we are briefely shown another problem on the electronic whiteboard:

Everytime she goes back in time something changes. We don't want her to learn the solution to the first problem just to be asked to solve this one! Homura-chan, here is the solution to this problem:

By the way, the technological level of the world they live in seems slightly superior to our own, but the same can be said for the problems they get in school considering they should be 14 years old!

In episode 9 we learned about entropy and the heat death of the universe and now we get these math problems. If the awesome story and shocking moments were not enough!
This anime never ceases to amaze me :D

By the way, can anyone help me with the translation of the left side of the whiteboard in this image?

I am tempted to try, but unfortunately my japanese level is not good enough yet and it will take me some time!

Pdf version of the solutions, if anyone is interested XD

Madoka Magica - 10 - Homura's story(ies)

Disclaimer: this post is made of spoilers.

Homura is in a time loop trying to save Madoka, her only friend, from becoming a puella magi.
It happens that this is not only her own wish, Madoka herself in one of Homura's many attempts asked to prevent her from making a contract with Kyubei.

The wish that started all

We all knew Homura was a time traveler and many already speculated she was in a time loop. After all, this would have gone well with her cold attitude. For her, this life is not the only one. She has made many attempts already and she doesn't care if something goes wrong. She can always restart if she doesn't like the outcome. She became cold after all her incredibly sad experiences... the fact she hasn't become a witch yet shows her determination.
She was close once, she was ready to give up and condemn the world to destruction, but Madoka saved her and gave her the strenght to continue, the will to not give up.

Homura will go on trying and trying until she finds a way out of the loop. Until she finds a way to save her only friend.

It also turns out Madoka's dream at the beginning of the series was Homura's last failed attempt, the one where Madoka defeated the Walpurgis Night with one hit and was on her way to become the incredibly strong witch who would destroy the world. It seems Madoka keeps some faint memory, at least she knew Homura's name.

One thing said by Kyubei makes me think that the world they live on might not be Earth, but only one of the many worlds used as power plants by the Incubators. He said even if this world is destroyed he didn't care since he collected energy already in excess of his quota. So they probably went the industrial way and increased the entropy-independent energy collection efficiency by planting humans in many worlds...

Above all this, and even if we were mostly expecting this development by now, I think the execution was awesome.

The way Homura trasformed from an extremely weak and shy girl to the powerful and cold puella magi she is now is told via her experiences. She saw her friend die so many times.
Her reaction in the last episode, all her behaviour until now makes sense. Including her hate for Kyubei.

She started out as an extremely weak puella magi. Her weapon? A golf bat :). She grew from a weak girl to this:

Her real strenght was her ability to stop time and she took advantage of it by preparing bombs. She expanded her arsenal after Sayaka's comment that her bombs were dangerous also for her allies. She razed armouries for guns (stopping time it's quite easy to loot everything). She improved to the point of being far above all the other puella magi, yet this is not enough to face the Walpurgis Night.

I was so worked up about Homura, but we also finally get to see Madoka as a puella magi! Her weapon is a bow and she is indeed strong.

Exagerated specula 1: Kyubei is using Homura to repeat Madoka's transformations and harvest infinite energy from her. I doubt it's true since Kyubei seemed to have no memories about the previous timelines, but we all know how manipulator he is. The possible "good" end is for them to break the loop and possibly save themselves.

Exagerated specula 2: Homura is the Walpurgis Night. She becomes a witch in the last timeline, the current one, after defeating herself. She sends herself to the past just before becoming a witch knowing that she would be defeated by herself and saving Madoka. This would be awesome, the ultimate sacrifice to break the time loop! The fact that her witch form existed in all timelines would be a consequence of her time abilities making her transcend time.
This is supported by the gears on the Walpurgis witch. The same gears that activate everytime she uses her power.

If they manage to keep up this level of awesomenes until the end for me this is going to be one of the best anime ever.

Ah, and the title should be "Puella Magi Homura Magica" :)

ISML 2011 Preliminary Period, Phase 1, Day 5 - My Votes and Results!

For three of the first 8 groups there is one character leading alone. They are very strong and are probably going to win. For the other 5 groups things are far from decided!

These are my votes:

And these are the results:

Reactions:

• (Group 1) Mio and Elsie first. Mio was indeed expected, but Elsie is the real exploit. She won in Arena 2 by a mere 8 votes over Asami! Merry is just behind with 10 points. In the next match Elsie will face Mio, so Merry and Elsie will most probably end up seconds together.
• (Group 2) Misaka is leading the group by herself with Ritsu, Last Order and Ikaros seconds. Ikaros was defeated by Last Order in Arena 1, she helped her onee-sama in getting the first place!
• (Group 3) Shinonono is still there with Shana, but next time the two will have to face each other and it will be hard for the haremette to defeat the flame haze! Saten wins in Arena 1 and grabs the second place. If all goes well she might keep it.
• (Group 4) Azunian wins over france-tan in Arena 1 and this was expected. The surpising thing is that the margin is not so high. Azusa won with about 3000 votes of difference the previous matches, this time they were less than 1000. This is a testament of the strength of Charlotte! Nymph shows that the good results of the Sora no Otoshimono characters was not random. She is now second with france-tan. In the last match she will face Azunian though, so Charlotte will be second alone.
• (Group 5) Hinagiku and Ika-Musume are leading the group and the last match will decide who will pass the preliminary phase! Judging by the quantity of the votes they get, Hinagiku has a definite advantage.
• (Group 6) Apparently this group is balanced since there are three characters first at 12 points. The truth is that they still have to face each other and they will do so in the next match. The first three positions will be decided there! Ui and Lingyin are very close, while Taiga is definitely the favourite.
• (Group 7) Yuki and Sora are leading the group. In the next match Yuki will probably take the lead and win the group.
• (Group 8) Haruhi won this group when she defeated Yurippe in the last match. The second place is basically also decided, as Index has to face the leader of the SOS Dan in the last match. So Haruhi first, Yurippe second and Index third.

Next match will see the second half of the groups!

ISML 2011 Preliminary Period, Phase 1, Day 4 - My Votes and Results!

With half the matches of the preliminaries done the balance of power starts to be clear. While there are still some strong characters who have not faced each other, for some to the groups the winner is almost already decided.

After seen so many strong characters from Hayate no Gotoku I started watching it :)
I can now support also Nagi and Hinagiku!

These were my votes for Day 4:

And these are the results:

Reactions:

• (Group 9) Its up to Ui and Victorica. i think Ui is still the favourite and the announcement of the new K-ON! manga can help even more. In Arena 2 Mikuru wins by a small margin on Laura. The last IS episode was not enough for german-tan to win, but still I think she gained a lot of support!
• (Group 10) Tsumugi and Konata lead the group, but they have not faced each other yet. Astraea and Nagi are close seconds and can still recover. It will be difficult to steal the first position though.
• (Group 11) Hellscyte-sama seems the favourite. She must pay attention to Tomoyo and C.C. who she will face in the next to matches.
• (Group 12) Yui defeats Saber! Seraphim wins in Arena 2 and Holo comes out first over Haruna by just 89 votes! This group really surprised me. It's the most balanced together with group 8. This victory for Yui probably gave her the first place.
• (Group 13) Another surprise here (for me at least!): Mami wins over Madoka, who comes out third in her arena! Kirino defeats Fate and takes the lead, the only real threat coming from Kyo.
• (Group 14) Kagami and Nagisa are first with 4 points of margin over the others. Only their showdown will decide the winner of this group.
• (Group 15) This is a group with 3 strong characters who have yet to face each other. Kuroneko, Senjogahara and Mafuyu are first with 4 points of distance from the seconds. I don't know about Mafuyu, but I still think Kuroneko is the favourite.
• (Group 16) Kanade is crushing any resistance! It will be very difficult for Rin and Nadeko to defeat her!

That's it for today!

ISML 2011 Preliminary Period, Phase 1, Day 3 - My Votes and Results!

The third day sees the second matches of the first half of the groups. These are my votes:

And these are the results:

Reactions:

• (Group 1) Mio is clearly favourite and Elfi is the only one keeping her pace with two victories. In the first Arena Merry suffers a defeat by the hand of Iwasawa!
• (Group 2) Misaka and Ikaros lead the group. Last Order shows what she is capable of when she doesn't have to fight her onee-san.
• (Group 3) Shana confirms the lead, but she must be careful of Shinonono. She is going to get some focus in the next IS episodes and might be a strong opponent. Saten-san wins by a good margin her Arena.
• (Group 4) There is little doubt that Azunyan will come out first of this group. The question is how big a threat france-tan can be. The latest IS episodes are focusing more on Laura and porbably the next will shift to Shinonono, so she might lose some power.
• (Group 5) Katsura is the favourite and Ika Musume wins by just 22 votes on Kiriya! She won also the first match by a few votes, now I doubt she can go against the Katsura.
• (Group 6) This group is one of the most equilibrated, but only because Taiga has not faced Ui and Lingyin.
• (Group 7) Yuki is in a strong position here, I don't think Kasugano Sora can defeat her.
• (Group 8) Haruhi won the showdown with Yurippe! Although the separation was only about 200 votes. I was also very divided between the two and only chose Haruhi because I support Kanade more (I know it's a stupid reason... I would have voted for both if only I could....)

Madoka Magica - 9

Usual disclaimer: this post is made of spoilers.

The full explaination from Kuybei:

• he is either a member or some device from an alien civilization
• this civilization searched for a way to contrast the increase of entropy of the universe and finally developed the technology to harvest entropy-independent energy from emotions (!!)
• they don't have emotions...
• they found out that puella magi emit big quantities of this kind of energy, the quantity going by the height of their emotions
• thus, they setup the contract thing to turn young girls (who happen to have the strongest emotions and produce the most energy) into puella magi:
• when they first become one getting a wish they emit energy from happines
• when they turn into witches they do also emit energy from grief

A nice little plan to contrast the entropy increase in the universe. Yet, it seems a little limited to resort to a single species living on a single planet, or have they planted humans in many other planets effectively using them as energy generators?
Anyway, let's not diverge to much...

Koyouko's sacrifice is the other big element in this episode. It seems the balancing of emotions happens also between puella magi. The most Sayaka was descending into grief, the most Kyouko regained her humanity and finally sacrificed herself to help Sayaka out of her misery.

Homura is the one who knows very well what is going on. The fact she suppresses her emotions looks like some protest against Kyubei too.

Madoka finally sees Kyubei as an enemy. I liked how the colors changed during his explaination to Madoka.

Kyubei has orchestrated everything to force her to to make a choice. With the incoming Walpurgis night she will either see Homura get killed or make a contract.
I seriously hope there is third option.

In the end everything sums up to Kyubei being a liar. If he could really grant _any_ wish he could just ask Madoka to wish for another mean of controlling entropy.

Madoka Magica - 8

This episode had so many shocking moments!

Spoilers:

• Madoka was very close to becoming a puella magi, but Homura saved her again killing Kyubei
• Homura in tears :’(
• Kyubei reveals to have many bodies. Another of his bodies appears and eats his own corpse
• Sayaka becomes a witch
• Kyubei's full name is Incubator
• Homura is a time traveler
• Kyubei reveals his true purpose: to make girls into puella magi. Puella magi grow into witches.

So the source of witches are puella magi themselves and Kyubei feeds himself with grief seeds.
There are also familiars that turn into witches so maybe once a puella magi turns into a witch she starts spawning familiars.
The one who killed Mami evolved from a familiar, yet she left a grief seed... It could be that familiars are generated by the grief seeds recycled by Kyubei while puella magi turn directly into powerful witches and can then spawn grief seed-less familiars and witches.

By the way, the Mami-killer was trying to eat them, it makes me think of Kyouko but ok...

The references to Sayaka's outfit by the witch in the first episode were shown since long and have now much more foundation.

I liked a lot the detail of Sayaka's lifeless body thrown away like a ragdoll when she finally turns into a witch.

Things are probably going downhill from now. With only 4 episodes left there is some time to collect all the loose ends!

ISML 2011 Preliminary Period, Phase I, Day 2 - My Votes and Results!

The results for Day 2 are out! This concludes the first Round.
But let's go in order, these are my votes for this day:

And these are the results:

Reactions:

• (Group9) Yui takes the lead as expected and Asahina seems to get quite some votes. Victorica is struggling a little bit, but she was against Ichinose from Clannad (and the other Clannad characters have won their arenas) and Laura german-tan. Laura could be getting more votes in the future depending on the next IS episodes. Poor Uiharu found Yui in her first arena :(
• (Group 10) Nagi gets the most votes with Tsumugi following closely. Konata wins her arena which also had Astraea and Mikan who could still do well in the future.
• (Group 11) Hellscyte-sama dominates her arena and Sakagami from Clannad does very well in hers. C.C. wins in the third arena and I wonder how she will do when pitted against these two.
• (Group 12) Yui from Angel Beats is doing good, followed closely by Saber. Haruna wins in her arena!
• (Group 13) If anyone still had doubts, Kirino is dominating this group. Fate is doing well too and Fujibayashi wins by a smaller marigin her arena.
• (Group 14) This group seems very equilibrated with all the characters taking less than 4000 votes (even less than 3000 in the third arena). Kagami seems the favourite for now, but in arena two Luise and Furukawa were not so far away.
• (Group 15) Koroneko wins by far and leads the group, but Senjogahara must not be underestimated.
• (Group 16) Kanade is the single character taking most votes in this first Round with 6009 votes! Nadeko and Rin can try as much as they want but it will be very difficult to defeat her!