Dragon Ball/Z/GT Fan Fiction ❯ The Next Bulma ❯ chap 1 ( Chapter 1 )

Gohan was sleeping and was awoken by his alarm clock AKA Goten.

"GOOOOHAN!!! MOM SAID IT'S TIME FOR BREAKFAST AND WON'T LET ME EAT UNTIL YOU WAKE UP! HURRY UP!" Said Goten then ran down the stairs.

Gohan ran down wearing his normal school clothes. He took his seat and started eating his pancakes. He looked at his watch and realized that he only had 30 minutes to get to his class.

"Bye! Mom! Goten be good ok?" Said Gohan

"Right Gohan!" Said Goten

"Goten! The Flying Nimbus is yours!" Said Gohan

Gohan flew to OSH and ran to the office.

"um… This is my first day here and I need to know where to go." Said Gohan

"What's your name dear?" Said the lady behind the desk

"Son Gohan…"

"Oh My…"

"Is there a problem?"

"No…It's just you got all of your answers right on your entry exam!"

"So…. Where is my class?"

"Right! It is Math with Mr. Smith, room 336[1]"

"We have another Bulma…"

Gohan walked to his room and knocked on the door and waited until Mr. Smith answered.

"Yes… Son Gohan. Come in…." Said Mr. Smith

"Class! I would like to introduce our newest member to our class. His name is Son Gohan and he got perfect marks on his entry exams. Only one other has done so. That was Bulma Briefs so I would watch how you treat him because he could be your boss someday." Said Mr. Smith The class laughed at the last sentence. "Did you know that Bulma's class had the same reaction? Most of her graduating class works for her. Gohan, would you like to say anything?"

"Well, when I'm not studying, I like to do martial arts." Said Gohan

"Like the bookworm could do martial arts!" Said Sharpner

"Sharpner! That's enough!" Said Mr. Smith "Gohan, you can take a seat next to Erasa."

The class was doing a problem on paper to solve it. Gohan was working on it and quickly found the answer. Erasa gave up on the problem and was drawing a picture of a mall.

"Erasa! Tell me your answer!" Said Mr. Smith

"x=7?" Said Erasa

"Nice try Erasa but the answer is actually…"

"No. The answer is 7." Said Gohan

"Mr. Son. If you are so positive of your answer, show us on the chalk board how to do it." Said Mr. Smith

Gohan walked down to the chalk board and proved that x would equal seven.

"… which shows that x=7." Said Gohan

The class looked dumbstruck at Gohan. Many have tried to do it but failed. He proved the great Mr. Smith wrong.

"So Gohan… Find three positive integers having the property that when you reverse the order of their digits, the numbers increase by a factor of exactly 4. For example 1234 would be transformed to 4321, but that is not quite four times as large." Said Mr. Smith

"If the original number is N = xy...zw its reverse is R = wz...yx. We must have either x = 1 or x = 2. If not, then multiplying by 4 would increase the total number of digits. Since wz...yx is a multiple of 4, it must be even so we must in fact have x = 2. Considering w as the leading digit of R, the possibilities are either w = 8 (if there is no digit to be carried) or w = 9 (if there is). But considering w as the units digit of N, we see that we must have w = 8 (since 4*9 = 36 , but we want the units digit of R to be 2).

Considering y to be the second digit of N, we see that y = 0, 1, or 2 (if it were larger, then there would be a carry digit and w, the first digit of R, would be 9 rather than 8). But considering y to be the ten's digit of R, we see that it must be odd, hence y = 1. A quick check shows that (...z8)*4 = ...12 forces z = 7.

We see that 2178 satisfies the necessary conditions and is hence the only such four-digit number.

For five-digit numbers we must have (21a78)*4 = 87a12 and a quick test shows that 21978 works. In fact, 219978, 2199978, ... all work.

In general, the numbers we seek have the form N1N2 ... Nk-1NkNk-1 ... N2N1 or N1N2 ... Nk-1NkNkNk-1 ... N2N1 where each of the Ni is of the form above. For example, 21782178 and 21978219997821978." Said Gohan

"Correct…Ann and Bob have the following conversation:

Ann: How old are your three kids, again?

Bob: The product of their ages is 36.

Ann: I can't figure it out from that information.

Bob: The sum of their ages is the same as your house number.

Ann: That's still not enough information.

Bob: The one who's older than the others has red hair.

Ann: Thanks! Now I've got it.

How old are Bob's kids?" Said Mr. Smith

The students in the class were dumbstruck and had one thought in their mind `how can anyone answer that?'

Gohan thought for a while mumbling different things until he said "Since Ann was unable to determine the kids' ages even though she knew the sum of their ages, the only possibilities occur when there is a duplicate sum, namely 9,2,2 or 6,6,1 (when the sum is 13). The fact that one child is older than the others eliminates the second possibility, so the children's ages are 9, 2, and 2"

"Last question, A bored student walks down a hall that contains a row of closed lockers, numbered 1 to 1024. He opens the locker numbered 1, and then alternates between skipping and opening each closed locker thereafter. When he reaches the end of the hall, the student turns around and starts back. He opens the first closed locker he encounters, and then alternates between skipping and opening each closed locker thereafter. The student continues wandering back and forth in this manner until every locker is opened. What is the number of the last locker he opens?"

"I thought these were going to be hard! Let's begin with a small example and work up to larger ones. Noting that 1024 is a power of 2, we will restrict ourselves to the situation where the number of lockers is a power of 2.

For two lockers, the student opens locker 1, then when he goes back down the hall, he opens locker 2.

For four lockers, after the first trip down the hall, lockers 2 and 4 remain closed. On the return trip down the hall, the situation is essentially the same as in the case of two lockers (except the student is moving in the opposite direction and the lockers have even numbers). Therefore the last locker will be the second one (going in the reverse direction), which is locker 2.

For eight lockers, after the first trip down the hall, lockers 2, 4, 6, and 8 remain closed. On the return trip down the hall, the situation is essentially the same as in the case of four lockers, so the last locker should be the second locker (in the reverse order), namely locker 6.

For sixteen lockers, the last locker will be the sixth locker among 2,4,6,8,10,12,14,16 in reverse order, namely locker 6.

At this stage, it would be handy to have a formula for the kth locker among 2,4, ..., 2n (in reverse order). It's not too hard to see that it's 2(n + 1 - k).

Continuing on, for 32 lockers, the last locker will be the sixth locker among 2,4,...,32, namely locker 2(16 + 1 - 6) = 22.

For 64, it's locker 2(32 + 1 - 22) = 22.

For 128, it's locker 2(64 + 1 - 22) = 86.

For 1024, it's locker 2(512 + 1 - 342) = 342. Which is our final answer.

"Son Gohan! Get out of my classroom now!"

"But what did I do?" Said Gohan

"Just go!"

Gohan gathered his books and papers and walked out the door. He walked down the hall to the office.

"Mr. Smith had me come here. What did I do?" Said Gohan

"Yes, Well you see, according to Mr. Smith, you started an insurgence in the class." Said the Principal.

"I did!?" Gohan looked surprised. "I only answered a series of questions, which got the students all acting weird." Said Gohan

"Another Bulma" muttered the Principal

"What?"

"Bulma had the same problem in school."

"Really?"

"A lot of teachers don't like opposition, you see…It's best not to answer too many questions in a class, it makes teachers extremely detest you - do you get what I'm saying?"

"I guess. I won't correct any teacher even if they are wrong again."

"Right. Get to class. You have biology next."

While Gohan was running to his next class, the teacher said "We can expect great things from you Mr. Son."[2]

So how was it?

[1] It was my math room

[2] They said that in Harry Potter. "We can expect great things from you Mr. Potter" I just saw it for the second time yesterday. I was watching it and pointing out things that were in the book and not in the movie and vice versa. I love the Harry Potter Series.

I got all of those weird questions from http://math.smsu.edu/~les/POTW.html they aren't mine. I can't do stuff like that… R/R!

Ja ne!