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The Question of the Day - ??? points

There are 3 hard questions of the day. Get all three right to earn an achvmt pkg!

Lucky Prime Hint! I am a 4-digit prime number that does not contain a 3.

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): What is the sum of the seven smallest composite numbers which cannot be determined to be composite simply by using the divisibility rules for 2, 3, 4, 5, 6, 8, 9, or 10?

Question of the Day 3 (No calculators): What is the value of 1.000000000000 + 2.000000000000 + 3.000000000 + 4000000000 + 5.000000000000000?

Previous Solution

The lucky prime was 89. Note that I create the lucky prime before I see the answers you wrote. This is not biased in any way.

The answer to yesterday's question was 225. No one got this question right.

Solution to yesterday's question:

The first step will be to find the prime factorization of 84 million. The prime factorization of 84,000,000 = 2^8 *3^1 * 5^6 * 7^1. Any number that is a factor of 84 million must have a prime factorization that uses the same prime factors raised to powers that do not exceed those from the prime factorization of 84 million. So a factor could have 2 as a prime factor with an exponent from 0 to 8, but because we want an ‘’even’’ factor, the number must be divisible by 2, meaning that the exponent of 2 cannot be 0. That gives us 8 choices (1 through 8) for the exponent. A factor of 84 million could have a 3 as a prime factor with 2 choices for the exponent (0 or 1). A factor of 84 million could have a 5 as a prime factor with 7 choices for the exponent (0 through 6). A factor of 84 million could have a 7 as a prime factor with 2 choices for the exponent (0 or 1). In total then, there are 8*2*7*2 = 224 numbers that would be an even factor of 84 million.

Yes, Blueeighthnote. Prime numbers are already not divisible by 4 or 7. I might give hints that will not help you.


1. Blueeighthnote: 2365 points (2 achvmt pkgs)

2. TimBluesWin: 655 points (1 achvmt pkg)

3. Imamadmad: 645 points (1 achvmt pkg)

4. Julianthewiki: 420 points (1 achvmt pkg)

5. 69.235...: 230 points (1 achvmt pkg)

6. ZombieBird4000: 50 points (1 achvmt pkg)

7. Supermario3459: 45 points (1 achvmt pkg)

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!)


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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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