Summary of my February 2021 Math mini-contest for D.Buzz 😎

Pixabay public domain image (geometry) 😀

This is my summary to my recently-held 28-day long Math mini-contest for D.Buzz. 😎

Even summaries such as this had taken me several hours to finish! 😅 That's because I had to prepare this manually. 😴

Participants

The active D.Buzz users who participated in the mini-contest were @jfang003, @eturnerx (@eturnerx-dbuzz), @ahmadmanga (@ahmadmangazap), and @holovision. There are a total of only 4 official participants. 4️⃣

There were also non-D.Buzz users who tried to participate in the contest. They are @appukuttan66, @paultactico2, @dkmathstats, @nathen007, and @minus-pi. Though they are still allowed to post their answers, they cannot become official winners for the day's problem, but they can be awarded a special prize like what @minus-pi obtained twice. 😁

@minus-pi won 1 HIVE twice as a special awardee for helping me make minor corrections on the solutions for my Day 20 and 21 Math problems! Even if the solutions were bit off, the answers remained the same! 😅

Winners

On the 28 contest days in February 2021, @jfang003 won a total of 14 days, @eturnerx-dbuzz won 4 days, and @holovision won 1 day. There was a total of 30 HIVE distributed, with a tiny excess to account for the rounding up to the nearest thousandth HIVE. 💰

Problems and solutions

Here comes the long part of this summary! 😅

(The days are hyperlinked to their problem page, and the answers to their solution page.) 👈

1In Hive, posts with pending payout rewards worth less than \$0.020 are "dusted" (not paid out) at payout time. How many rational numbers are there between 0.000 and 0.020?no answer@holovision
2On the Cartesian plane, Vision and Fang are respectively at (10,2) and (3,6). Manga is above them and is twice as far from Fang as Vision. What is the position of Manga?many possible answersnone
3Holovision's 4-dimensional holographic technology enables him to interact with a tesseract. He wants to attach to it a 4D cord at its two opposite corners. If each of the tesseract's sides is 4 meters long, how long should his cord be?8 meters@jfang003
4Jan Charles plans to buy pizza for D.Buzz. With exactly ₱15,000 without change, he can buy either 15 bacon pizza boxes and 12 chicken pizza boxes, or 10 bacon pizza boxes and 18 chicken pizza boxes. How much is a box of chicken pizza?₱500@jfang003
5Fang and Vision are on a circular race track 3,183 meters in diameter. Fang runs 2 meters per second while Vision runs 2.5 meters per second. They start running in the same direction from opposite points on the track. How many hours does Fang need to be beside Vision?2.78 hours@jfang003
6Chris wants to randomly get candies from a bag. There are 5 flavors of candies there, and there are at least 2 pieces of each flavor. What is the minimum number of candies he must get to ensure he gets 5 pairs of matching flavors?14 candiesnone
7Manga is 5.75 meters from both Fang and Vision. The angle formed by Fang and Vision with Manga as the vertex is 32.5°. How far is Fang from Vision?3.22 metersnone
8Holovision waits until 11:00 P.M. in his local time to answer Math problems. When he looked at the clock just after 10:00 P.M., he noticed its hour and minute hands pointing in opposite directions. How many exact minutes does he still need to wait?38 2/11 minutes or 38.18 minutes@jfang003
9Jan Charles thinks whether a 20-inch pizza cut in 8 equal slices gives a bigger slice than a 17-inch pizza cut in 6 equal slices. Which pizza gives a bigger slice, and by what percentage is the bigger slice larger than the other?3.81%@jfang003
10In an on-site Math contest event for D.Buzz with 10 participants seated around a circular table, how many ways can the participants be seated such that the participants Manga, Fang, and Vision are not beside each other?300 waysnone
11In a horse race, holovision's intelligent camera counts horses with human riders. However, the camera malfunctioned, so it instead counted 170 feet and 50 heads, including horses without riders but not riders without horses. How many riders are there?15 riders@eturnerx-dbuzz
12Jan Charles is running on a mountain. He can run downhill with an average speed of 15 kilometers per hour (kph) and 9 kph uphill. What will be his average running speed on flat ground?12 kilometers per hour@jfang003
13A Hive user wants to Power Down, which converts 1/13 of the Hive Power (HP) to HIVE per week (the converted HP is gone). If he has 3,230 HP and started to power down to 1,000 HP, how much HP will he still have on the 10th week?1,686.15 HP without interest or > 1,686.15 HP with interest@jfang003
14Ahmad wants to make new orange paint colors using two orange paints A and B of different concentrations (%). Two parts A and one part B produces 54.67%, while 3 parts A and 2 parts B is 52.80%. What are the percent concentrations of Paints A and B?Paint A = 64.02%; Paint B = 35.97%@eturnerx-dbuzz
15Jan Charles threw a frisbee with initial velocity of 15 meters per second from mountaintop 3 kilometers high from sea level, 30° from horizontal. Assuming no air resistance and obstacles, after how much time will the frisbee be at sea level?25.53 secondsnone
16A Hive user wants to invest HIVE at 15% annual interest compounded daily. How much HIVE does the user need to invest to earn 250 HIVE after 30 days?19,879.43 HIVEnone
17Ahmad decided to play with numbers. Starting at a positive real number, he adds 6 and gets the square root of the sum. The addition of 6 and getting the sum's square root is repeated indefinitely. What number will the result approach?3 and -2none
18Jan Charles, using his personal jet, can fly 300 kilometers in the direction of the wind in 2 hours, and 3 hours when directly against the wind. What is the speed of the wind?25 kilometers per hour@jfang003
19A Hive community is hosting a Math contest with a predetermined number of participants. If a new participant enters the contest, 1/10 of the community are participants; if a participant leaves the contest, 1/13 of the community are participants. What is the original number of participants?no answer@eturnerx-dbuzz
20Turner placed a square canvas roof 16 square meters big above level ground as shade. However, one of the roof's corners was placed 1 meter higher than the others. If the sun is shining directly above, what area of the ground is shaded by the roof?no answer@jfang003
21Jan Charles threw a paper airplane whose trajectory is y = 2 - (x-5)² / 16, where y is the kilometers above sea level and x is the horizontal distance in kilometers from Jan Charles. After flying for 2 kilometers horizontally, what is the angle of elevation of the plane?22.02°none
22Holovision is lost in hyperspace at (15.6, 12.4, 8.9, 6.66) and needs rescue. His interdimensional portal generator at (3.84, 5.16, 4.20, 0) needs the distance to pull him back into this universe. What is Holovision's distance from the generator?16.04 units@jfang003
23Fang and Manga play Rock-Paper-Scissors. Fang has a 32%, 34%, and 34% of choosing Rock, Paper, and Scissors, respectively; Manga has 29%, 39%, and 22%, respectively. What is the probability of Fang winning a match (against Manga)?30.16%none
24Turner decided to power up a lot of Hive Power (HP) by vesting 500 HP on the first Monday, 510 HP on the second Monday, 520 HP on the third Monday, and so on. On which Monday would he have already vested at least 100,000 HP without HP inflation?101st Monday@jfang003
25A basketball hoop is at the top of a 5-meter pole perpendicular to the ground. Fang is 13 meters away from the hoop itself. Manga stands midway between the base of the pole and Fang. The ground is horizontal. How far is Manga from the hoop itself?7.81 meters@jfang003
26Fang bought a rectangular cake with icing on all sides except the bottom. He then cut the cake into 6 by 8 by 5 cubes. How many of the cake cubes will have at least 2 sides with icing?40, 42, or 46 cubes (any of the above)@eturnerx-dbuzz
27Fang, Vision, and Manga are solving for missing values of the triangle ABC. Fang was able to get sin (A) = 4/5, while Vision got sin (2A) = 19/20. Manga needs to solve for cos (A). What is the exact value of cos (A)?19 / 32 or 0.59375@jfang003
28Chris wants to help his nephew with a Math question. The question asks for the slope of the line whose equation is y = 2x + 3. What is the answer to the question?2@jfang003

Final words

The only sentence I could say is... the event was so tiring but fun. For every day in the mini-contest, I spend 1 to 4 hours making a Hive-themed, not-too-difficult Math problem, plus its answer and solution.

I currently have a plan to host another mini-contest for D.Buzz, but with slight changes to the rules such that anyone can officially become a participant by just publishing a (non-spam) post or comment on D.Buzz within the last 24 hours before submitting the answer for the day's problem, and that the mini-contest will run only for 7 days to avoid fatigue for both the host and participants. Please note that this is still a plan.