Somewhere last week from March 22 to March 30 (UTC +8) this year, I held a week-long (7-day) Math mini-contest for D.Buzz (rules here) after enough encouragement from its participants and a D.Buzz admin!

Listed below are the Math problems I asked, together with their answers. Each problem and solution is hyperlinked to their corresponding post and comment, respectively.

Day | Problem | Answer | Winner |
---|---|---|---|

Day 1 | In a game within a Hive community with 20 participants, each participant provided a random number from 1 to 100 inclusive. What is the probability that any two participants share the same random number? | 86.96% | none |

Day 2 | In a contest, Ahmad (A) must guess where the hidden prize is in 10 baskets to win. After A guessed, the host removed 5 empty baskets and offered A the chance to switch baskets. If A has a 70% chance of switching, what is the probability that he wins? | 18.75% | none |

Day 3 | Fang participated in a Math contest. At the end of the contest, the average of all the participants' scores is 90. If Fang did not participate, the average score will have been 88. What is Fang's score? | (many answers) | @appukuttan66 |

Day 4 | Ahmad played with numbers again. Starting with a positive number N, he added 3, then used the sum to divide N. The addition of 3 and using the sum to divide N is repeated indefinitely. What number will the result approach? | 0 | @ahmadmangazap |

Day 5 | Chris has 8 times ₱50 bills than ₱500 bills, and 50 less ₱200 bills than ₱50 bills. The total value of those bills is ₱15,000. How many ₱200 bills does he have? | 30 | @jfang003 |

Day 6 | In a D.Buzz gathering, 32 seats have been prepared such that there are 4 rows and 8 columns. How many ways can Turner and Vision be seated such that they are not adjacent to each other horizontally, vertically, and diagonally? | 804 | @minus-pi |

Day 7 | Holovision's hemispherical dome for his holography project needs painting. The diameter of the sphere is 3 meters long. If he covered the hollow part with flat cardboard, what is the surface area of the hemisphere? | 6.75π or 21.21 square meters | @minus-pi |

Thanks to all participants and supporters!

### Participants

- @minus-pi (won twice) 🏅🏅
- @jfang003 (won once) 🏅
- @ahmadmangazap (won once) 🏅
- @appukuttan66 (won once) 🏅
- @eturnerx-dbuzz
- @fallingforwards
- @harpreetjanda

**Special mentions:** @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯