Shikamaru's Maths Challange

Read the IQ Challenge here. To take up the challenge, email Shikamaru your answer at

Other answers to this question : Main, Pg 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2


Challenge #04 - Training at the Academy

Your Answers ----------------------------------------

(27/11) Cel : I'm tired, i've been up for a few hours trying to figure this out, it's not a hard question but you worded things a little too confusing.  I'm thinking the IQ of 200 goes to quick thinking and not "english".  Well besides the confusion, you have stated the following, unless you did not make it clear, which in turn will be your own fault:

There is 4 squads.  You said they were divided into squads of 4 (normally anyone who reads that understands 4 people per group, which then the answer would be zero, obviously if it was so simple, you wouldn't have bothered asking it at all) but then you go and tell someone that you never said they were in groups of 4, so that sentence you wrote implies the OTHER possibility, which means there is only 4 squads of X number of ninjas.

Now that we know there is 4 squads for ROUND 2, a few things are a little confusing on the rules.  For example:

"Round A : The students are allowed to fight against anyone and as many opponents they choose. (i.e. 1 nin can go against 5, or 3 can go against 7) However, the nins cannot change opponents. "

That's fine, you're stating that the number of combatants can be from 1 to max remainder.  However, if the rest of the people don't want to fight alongside others to fight just one person, then that means that the single person who decides to fight EVERYONE, will be out of ROUND 2, indefinetely.  But we don't know who or how many fought in round 1, so this is just assumption of a possibility.  Regardless, the number so far is at least 1 person would be left out if he or she was so reckless as to want to fight everyone.  Now here is where it gets too confusing:

"Round B : The students must not spar with the opponents encounted in the previous round and must spar with all those they didn't fight in the first round."

Besides spelling "encountered" wrong, you state that they "must spar ALL those they didn't fight".  You can try to argue that you didn't mean ALL of them literally, but that's exactly what that sentence is implying.  So already, the ninjas can't team with any of their teammates on ROUND 1, because they have to spar them.

Now that they can't team with their own guys, they have to team with the ones they already fought.  But those that they already fought, can't team together either and have to fight their own teammates.

Now it seems like it's gonna be a lot more than just 4 squads, and it seems like it'll be more individual people than anything, BUT Iruka says that the table will be identical.  All he has to do is re-label the students.... the students, what does that mean? that he's gonna go out there and change everyone's numbers? that's cheating himself, either that or you meant that he'll have to re-label the table.  You really need to word your sentences better.  If this is really all the information you have provided, people have already shouted the answer, it's either none are left over which implies by every single fact that you have given, or there is a CRAP load of people that are gonna be not fighting on the second round.  Yet you're looking for a value?.. I don't understand why you ask for a value if you didn't give any yourself besides "4 squads".

While I should say that the answer SHOULD be NONE, because Iruka said the tables are IDENTICAL (as in equal in the number of combatants and ammount of them, identical in every way possible), that means there should be NONE left out.  But you keep arguing that if it was that simple, then you wouldn't have asked.  This is starting to be more of a trick question than a real math problem because you failed to word it correctly.

You already denied 1, 2, 3, 4, and 0 are incorrect.  You also told others that 10 and 12 that you just fail to see their reasoning or that you don't understand them.  After thinking about it for a while, I realized that the squads in ROUND 2 (since there is 4 squads), they cannot be composed of more than 2 people in each squad, then I realize that they could be, because if a squad of 1 or 2 people in ROUND 1 wanted to, they could fight any enemies they wanted, regardless of the other squad's wishes.  So if Naruto wanted to, he can just pick random opponents from each squad individually. So since he mixed and matched, there could be a squad that he picked to fight 2 opponents, so it's possible for him to team up with 3 people... but i'm still getting confused, because I go back to that damn word, "IDENTICAL".

So 4 squads eh?...identical to round 1.... all those squads could have done a free for all (1vs2vs3vs4) because then they would only need to fight their own team which would be composed of anywhere from 1 to X number of teammates, if that's the case then all ODD numbered teammates would be out of the game, SIMPLY because you insist there is some left out.  So THERE has to be some left out, (otherwise you wouldn't have asked how many possible guys would be out)

Let's assume this is a possible combination..for all these squads fighting each other (assuming the whole "each fighter picks their own guy to fight" rule doesn't apply fully, because the answer would be a non-specified number already)

Free for all:

SQUAD A: 1-2-3-4-5

SQUAD B: 1-2-3-4-5-6-7

SQUAD C: 1-2-3-4-5-6

SQUAD D: 1-2-3

All the number 1's would be in squad 1.

All the number 2's would be in squad 2.

All the number 3's would be in squad 3.

All the number 4's would be in squad 4.

All the 5's, 6's and 7's can't be in their own squads because there is only 4 squads.  And they can't be in a team with at least 1 person they already teammed with because the rules say that they have to fight everyone else they didn't fight on round 1. and the rule says ALL.  So if there is only 4 squads, that means at least more than 5 will be left out.

But this is all if it was a free for all, there is no real decisive fight mode that they chose.  For all I know, it could've been squad A vs C, and squad B vs D, then the number of people that they can party with would be only 2 per team or so, back to the beggining.  I'm tired of this, I can't hit on the mark because there trully is insufficient data, or the data is worded incorrectly to a person who does not know the answer first hand.

Shika : Squads of 4 means 4 in each squad. And in the 2 rounds of fighting there are no teammates. If a no. of people happened to be fighting the same guy, that doesn't mean they are allies, it's every man for himself. The point of the question is that there is a certain no. of people, and it is common knowledge that any number leaves a remainder of 0 to 3 when divided by 4. Some of these remainders are not possible given the information provided. Just take away those and you'll have your answer. There. I'm being philanthropic. (Like I said before, reading other people's postings before answering can be quite rewarding). Next!


(26/11) Kellianne : Is it possible that the answer is everyone will be left out sometime or another, because people can fight however may people they choose, right?

Shika : maybe you should state your difficulty. Most problems are solved by asking the right questions


(21/11) Punky : Hello! I'm not really sure I understand the question but I want to make a guess anyways ^_^  Could the answer be 0-3, since you don't ask for an exact number?  I'm guessing this by using the logic that if you have more than four left over then you would have another squad.

Shika : maybe you should state your difficulty. Most problems are solved by asking the right questions


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