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ACHIEVEMENTS EARNED DURING THE LAST QUESTION: 0

## The Question of the Day - ??? points

Lucky Prime Hint: I am an odd 2-digit prime number.

Blueeighthnote, I am letting you try to complete the first question of the day.

Question of the Day 1 (Calculators are permitted): Lilly orders a large, orange pineapple-flavored ice cream at the Ice Cream Shack. She immediately realizes that it would be too big for a cone, so she asks them to place it in a cup. Each scoop of ice cream is a perfect sphere with radius 3 inches (a specialty of the Shack). The cup the ice cream is placed in is a cylinder with diameter 7 inches and height 10 inches. If the scoops are gently placed in the cup, a large (3 scoops) would not fit in the cup, so the scoops are pressed into the cup so that all the ice cream fits under the lid. How many centimeters are in the minimum possible height of the ice cream in the cup? Express your answer to the nearest tenth.

Question of the Day 2 (Calculators are permitted): Each of Jonathan's bicycle tires revolved 2327 times as he rode three miles. What is the diameter of one of Jonathan's bicycle tires, in inches? Express your answer to the nearest whole number.

## Previous Solution

The lucky prime was 1229.

QUESTION OF THE DAY 1: ANSWER TEMPORARILY WITHHELD

QUESTION OF THE DAY 2: To be composite, a number must be the product of two natural numbers greater than 1. Since we want the 7 smallest that also aren't divisible by 2, 3, 4, 5, 6, 8, 9, or 10, the smallest factors the numbers could be divisible by are 7, 11, 13, 17, 19... The smallest composite numbers divisible by 7 but not any of the other numbers are 49, 77, 91, 119, 133, etc. The smallest composite numbers divisible by 11 are 121, 143, 187, etc. Together, the smallest 7 are 49, 77, 91, 119, 121, 133, and 143. The sum is 733.

QUESTION OF THE DAY 3: CORRECT

## Scoreboards

1. Blueeighthnote: 2390 points (2 achvmt pkgs)

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8. Wildoneshelper: 40 points (1 achvmt pkg)

9. Emmaelise401: 30 points

9. CalzoneManiac: 30 points

11. Googleaarex: 10 points (Here are 10 points to get you started!)

## Achievements

### Skills 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

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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.

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

### Sun Badges

All epic ones are found here.

### Galaxy Badges

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

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### Trustworthiness Badges

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

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### Duration Badges

Yes! YOU KNOW IT! PARTICIPATION EVERY DAY!