Question of the Day! August 28 ~ 30

The following questions can be answered in the next three days!

Hi, everyone!

As no one answered the questions during August 21 and August 27, the time has been extended. The following questions can be answered until August 30, 12:00 pm (UTC).

Questions[]

1. How many prime divisors does the number 43659 have? Remember to apply the divisibility rules! [15 points]

2. If $log_x16 = 2$ , then x = ? [15 points]

A) 1/8
B) 8
C) 32
D) 4

3. a, b, c are all real numbers. For the following system of linear equations, which of the following are correct? There are multiple correct choices. [60 points if all correct; 36 points if 1 is incorrect, and 12 points if 2]

${\displaystyle \begin{cases} x + 2y + az = 1 \\ 3x + 4y + bz = -1 \\ 2x + 10y + 7z = c \end{cases}}$

A) (If there is a solution) Exactly one set of answers is available.

B) (If there is a solution) 11a - 3b ≠ 7

C) (If there is a solution) c = 14

D) (If there are no solutions) 11a - 3b = 7

E) (If there are no solutions) c ≠ 14

Bonus: Lucky Prime Hint: Less than 200, a number that can use the right trim 1-digit ±6 (only one of them can apply!) to find out the divisibility.

Previous Answers (8/17 ~ 20)[]

For number 1: The answer was actually "E". However, I just noticed that the display of these numbers made them look confusing, as if they were regular numbers. The smaller numbers on the right were all exponents. The way the number is displayed makes it look like $(\dfrac{1}{8}) - 2$ , and that affected the answers so much that I have to award points for free, despite that the answer B alone is certainly very large, due to $(\dfrac{1}{8})^{-2} = (2^{(-3)})^{(-2)} = 2^6 (= 64)$ , making it the least likely answer at the start.

Anyone who has answered this question can earn points.

To sort out the numbers' order, the solution is to convert all numbers into $2^n$ , and then compare it from there.

The order was: $(\dfrac{1}{8})^{-2} (B) > 2^{\tfrac{1}{3}} (A) > 2^{-\tfrac{1}{4}} (C) > (\dfrac{1}{2})^{\tfrac{1}{2}} (D) > 8^{-\tfrac{1}{3}} (E)$

For number 2: Correct! ALPHA is less than DELTA.

For number 3: When x equals 0, the value is 9.

For number 4: Correct! The answer was indeed 150, because as it is a 3-digit number, x cannot be 0. As y can be any digit from 0~9, there are 10 numbers each from 2y0, 1y3, 3y1, 2y4, 4y2, ...... 7y9, 9y7.

Leaderboards[]

1. Blueeighthnote: 13843 points (2 achvmt pkgs) - One more to get the next lucky prime badge!
While being the host, the host cannot earn any points during the period.

2. Minipop56: 12206 points - Four more to get the next lucky prime badge!

3. TimBluesWin: 755 points (1 achvmt pkg)

4. Imamadmad: 745 points (1 achvmt pkg)

5. Dalek-James: 730 points

6. Julianthewiki: 525 points (1 achvmt pkg) - RETIRED

7. Lefty7788: 300 points - One more to get the next lucky prime badge!

8. Wikia Contributor 69.235...: 230 points (1 achvmt pkg)

9. Supermario3459: 145 points (1 achvmt pkg)

10. 3primetime3: 87 points

11. ZombieBird4000: 50 points (1 achvmt pkg)

12. Wildoneshelper: 40 points (1 achvmt pkg)

13. Emmaelise401: 50 points

14. CalzoneManiac: 30 points

15. 21qmcgagin: 20 points

16. Kyodaisuu: 21 points

17. Googleaarex: 10 points

Achievements[]

The Badges will still be continued further.

Skillz Badges![]

Usually awarded for having skills to solving hard questions, etc.

1. Quick Thinker! (+10 points) - Awarded for posting an answer before I write "Please leave your answers here." FIRST FOUNDED BY BLUEEIGHTHNOTE

2. RARE: Leaderboards Expert! (+300 points) - Awarded for being 1st place on the leaderboards for 30+ days. FIRST FOUNDED BY BLUEEIGHTHNOTE

3. RARE: More than a Millenium! (+100 points) - Awarded for being first in the leaderboards and scoring more than 1000 points from the runner-up. FIRST FOUNDED BY BLUEEIGHTHNOTE

4. Questions in a question (+20 points)? Awarded for finding three ambiguities in a single question. EARNED BY IMAMADMAD

Earth Badges[]

Most rare ones are found here.

1. RARE: Top Ten (+30 points) - Awarded for being the first top 10 people ONLY to participate on the question of the day! EARNED BY THE FIRST 10 PARTICIPATING PEOPLE

2. RARE: Cyclone Centurion! (+250 points) - Awarded for scoring at least 10000 points in the QOTD system! FIRST FOUNDED BY BLUEEIGHTHNOTE.

Sun Badges[]

All epic ones are found here.

1. EPIC: Lucky Primer (+100 points): Congratulations! You have guessed the lucky prime correctly. Get the Lucky Prime two more times to earn the next achievement! FIRST FOUNDED BY JULIANTHEWIKI.

2. EPIC: Very Lucky Primer (+200 points): Congratulations! You have guessed the lucky prime correctly two more times. Get the Lucky Prime three more times to earn the next achievement! FIRST FOUNDED BY MINIPOP56 AND BLUEEIGHTHNOTE.

3. REALLLLY LUCKY PRIMER (+300 points): Congratulations! You have guessed the lucky prime correctly three more times. Get the Lucky Prime four more times to earn the next achievement! FIRST FOUNDED BY MINIPOP56.

4. EPICEPIC: First of 2015! (+350 points): Congratulations for being the first to answer the questions in 2015 QOTD! FIRST FOUNDED BY DALEK-JAMES.

Galaxy Badges[]

Mysterious badges from a far-out universe. Each one found here is worth 10000+ points and/or 5+ achievement packages.

1. MYSTERY: ATLAS (+10000 points) - ??? FIRST FOUNDED BY BLUEEIGHTHNOTE.

2. FOUNDER: TIME KEEPER (+0 points) -- Being the host of QOTD for more than 1 year! Special thanks to your dedications! FIRST FOUNDED BY 3PRIMETIME3!

Uniqueness Badges[]

Unique things one can do in the answers section. ONLY ONE PERSON CAN EARN EACH BADGE.

1. Analyzer! (+10 points) - Awarded for drawing a diagram. FOUNDED BY IMAMADMAD

2. Inspiration! (+5 points) - A question was dedicated to you! FOUNDED BY BLUEEIGHTHNOTE

Trustworthiness Badges[]

Awarded by how much I trust someone on this wiki. Please do not ask me about these badges.

1. Reliability (+100 points) - Trusted to write a question of a day. FIRST FOUNDED BY BLUEEIGHTHNOTE, AND IMAMADMAD

2. Scoreboard Tinkerer (+100 points) - Trusted to change the scoreboards. FIRST FOUNDED BY BLUEEIGHTHNOTE AND JULIANTHEWIKI

3. Prime Staff (+100 points) - Become a chat moderator, rollbacker, sysop, or bureaucrat on this wikia! FIRST FOUNDED BY BLUEEIGHTHNOTE, JULIANTHEWIKI, TIMBLUESWIN, IMAMADMAD, SUPERMARIO3459, MINIPOP56, AND DALEK-JAMES

Duration Badges[]

Yes! YOU KNOW IT! PARTICIPATION EVERY DAY!

1. 4-Leaf Clover! (+100 points) - Awarded for participating on the Question of the Day everyday during the month of March! FIRST FOUNDED BY MINIPOP56.

2. April Fools! (+100 points) - Awarded for participating on the Question of the Day everyday during the month of April! FIRST FOUNDED BY MINIPOP56.