
3
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Minipop's question:
Bob has a fourdigit number. When he reverses the order of the digits and adds it to his original number, he gets a number that is 990 less than a perfect cube and is not divisible by 3 or 16. His original number's first digit was prime and odd. If his original number was not divisible by 5 and if it didn't repeat any digits, then how many possibilities are there that his original number could be? Name 3.
1. Blueeighthnote:…
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Minipop, you wanted to make the next question?
sqrt(2). Message me if you want to know why.
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2. Minipop56: 11765 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...: 230 points (1 achvmt pkg…
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If regular octagon ABCDEFGH has sides of length 2 cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form.
Same question as yesterday.
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2. Minipop56: 11750 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewik…
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If regular octagon ABCDEFGH has sides of length 2 cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form.
25.
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2. Minipop56: 11750 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt …
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A circle with a radius of 4sqrt(3) is inscribed inside a regular hexagon. What is the area of the hexagon? Express your answer in simplest radical form. Solve this question instead: What is 5^2?
Same question from yesterday.
1. Blueeighthnote: 13790 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11735 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 7…
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A circle with a radius of 4sqrt(3) is inscribed inside a regular hexagon. What is the area of the hexagon? Express your answer in simplest radical form. Solve this question instead: What is 5^2?
192 sqrt(3)/2
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3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 ach…
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Now, for the QOTD. A circle with a radius of 4sqrt(3) is inscribed inside a regular hexagon. What is the area of the hexagon? Express your answer in simplest radical form.
32 8/11. Message me if you want to know why.
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4. Imamadmad: 745 poi…
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PRIME STAFF AND RELIABILITY REWARDED TO DALEKJAMES.
At 3:00, the hour hand and minute hand of a 12hour clock are perpendicular. What is the least number of minutes that must elapse for this to be true again? Express your answer as a mixed number.
30, 31, 32 and 33. Message me if you want to know why.
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DalekJames, you wanted to make a question. Making a question will earn you a Trustworthiness badge!
756. Message me on my message wall if you want the solution.
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4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvm…
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The solutions of x^363x^2+cx1728=0 form a geometric sequence. What is the value of c?
Same question as yesterday.
1. Blueeighthnote: 13775 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11720 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...:…
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The solutions of x^363x^2+cx1728=0 form a geometric sequence. What is the value of c?
Same question as yesterday.
1. Blueeighthnote: 13775 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11720 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...:…
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The solutions of x^363x^2+cx1728=0 form a geometric sequence. What is the value of c?
93. Please message me on my message wall if you want the solution.
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2. Minipop56: 11720 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg) …
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What is the sum of the squares of the solutions of x^315x^2+66x80=0?
71/72. Please message me on my message wall if you want the solution.
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3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wik…
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Use 7 different digits hosen from 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make two fractions. Take the sum of the two fractions. What is the largest possible sum you can create that is less than 1? express your answer as a common fraction.
12.
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3. TimBluesWin: 755 points (1 achvmt pkg) …
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If the sum of 8 consecutive integers is 68, then what is the largest of the integers?
30%
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2. Minipop56: 11695 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...: 230 points (1 achvmt pkg)
7…
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The area of a square is increased from 60 sq. cm to 101.4 sq. cm. By what percent have the side lengths been increased?
Same question.
1. Blueeighthnote: 13770 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11695 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Con…
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The area of a square is increased from 60 sq. cm to 101.4 sq. cm. By what percent have the side lengths been increased?
Same question.
1. Blueeighthnote: 13770 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11695 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Con…
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The area of a square is increased from 60 sq. cm to 101.4 sq. cm. By what percent hav eth eside lengths been increased?
60,480.
1. Blueeighthnote: 13770 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11695 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributo…
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The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 are each used once to form a positive ninedigit integer. There are 362,880 possible 9digit integers like this. How many of them have the digits 1, 2, and 3 in order from least to greatest throughout the integer? One example is 451, 728,936.
Same question as yesterday.
1. Blueeighthnote: 13755 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11680 points  One more …
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The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 are each used once to form a positive ninedigit integer. There are 362,880 possible 9digit integers like this. How many of them have the digits 1, 2, and 3 in order from least to greatest throughout the integer? One example is 451, 728,936.
When 5 coins are tossed, the distribution of the number of heads and tails follows the 5th row of Pascal's triangle. There is 1 way to get 0 heads, 5 ways to…
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Five coins are tossed and at least one of them landed on heads. What is the probability that more than one of them landed on heads? Express your answer as a common fraction.
3.
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2. Minipop56: 11565 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 …
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Five coins are tossed and at least one of them landed on heads. What is the probability that more than one of them landed on heads? Express your answer as a common fraction.
3.
1. Blueeighthnote: 13755 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11550 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 …
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X2 Quick thinker: Minipop56 and Blueeighthnote
There is no question of the day today.
4.
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2. Minipop56: 11535 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...: 230 points (1 achvmt pkg)
7. …
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A regular hexagon and a regular octagon have the same perimeter. If the side lengths of these polygons are whole numbers and the sum of the perimeters is less than 200, how many different pairs of hexagons and octagons can be made?
68.
1. Blueeighthnote: 13715 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11510 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. …
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Solve this question instead of the one printed below. What is 9*84?
What is 35% of 14% of 19% of 198405? Express your answer to the nearest hundredth.
I rewarded Minipop the points!
1. Blueeighthnote: 13715 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 11495 points  One more to get the next lucky prime badge!
3. TimBluesWin: 755 points (1 achvmt pkg)
4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: …
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Hey guys! Good job on the checkpoint! Blueeighthnote, I rewarded you 100 extra points for catching the error.
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I have rewarded bonus points to Blueeighthnote and Minipop. I did not count incorrectly!
I don't have a question in mind, so I will take a question from my textbook :)
A cone of height H with a base of radius r is cut by a plane parallel to and h units above the base. Find the volume of the solid (frustum of a cone) below the plane.
If any…
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Achievements earned during the last question: 2
1. MYSTERY: ATLAS (+10000 points)  ??? FOUNDED BY MINIPOP56
2. RARE: Cyclone Centurion! (+250 points)  Awarded for scoring at least 10000 points in the QOTD system! FOUNDED BY MINIPOP56
PLEASE ANSWER THE QUESTIONS TO THE BEST OF YOUR ABILITY. I WILL ADD THE POINTS ON THE SCOREBOARDS WHEN APPROPRIATE:
 Blueeighthnote: 40 points ( achvmt pkg)
 Minipop56: 70 points ( achvmt pkg)
 TimBluesWi…
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Please show your work!
Suppose a, b, and c are integers that satisfy the system of equations
(a^2)b + (b^2)c + (c^2)a = 2186
(a)(b^2) + (b)(c^2) + (c)(a^2) = 2188
Evaluate a^2 + b^2 + c^2.
Lucky Prime Hint: 8
I didn't know the answer to that one. That was a question from one of my previous math competitions. But I know the answer to this one!
1. Blueeighthnote: 13555 points (2 achvmt pkgs)  O…
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X1 Quick Thinker (founded by Minipop56)
Please show your work!
Three mutually tangent spheres each with radius r = 5 sit on a horizontal plane. A triangular pyramid has a base that is an equilateral triangle with side length 6, has three congruent isosceles triangles for vertical faces, and has height h = 12. The base of the pyramid is parallel to the plane, and the vertex of the pyramid is…
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If A(X^2) + B(X) + C = 0, solve for X in terms of A, B, and C. Remember there is no partial credit.
42sqrt2
1. Blueeighthnote: 13555 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 970 points  One more to get the next lucky prime badge!
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4. Imamadmad: 745 points (1 achvmt pkg)
5. Julianthewiki: 525 points (1 achvmt p…
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Achievements earned during the last question: 8
X1 Skillz Badge: Quick Thinker! Founded by Minipop56
X7 Trustworthiness Badge: Prime Staff!
Blueeighthnote, was Minipop right?
Four unit circles are centered at the points (1,1), (1, 1), (1,1), and (1, 1). A fifth circle centered at the origin, does not overlap any of the other circles and is tangent to all four of the unit circles. The area of this fifth circle is Aπ square units. Wh…
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X1 Skillz Badge: Quick Thinker! Founded by Minipop56
X7 Trustworthiness Badge: Prime Staff!
Blueeighthnote, Another time for you to create the question of the day and lucky prime (if you want to). This question will go on for the rest of 04/14.
36.
1. Blueeighthnote: 13555 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 930 points  One more to get the next …
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Achievements earned during the last question: 8
X1 Skillz Badge: Quick Thinker! Founded by Minipop56
X7 Trustworthiness Badge: Prime Staff!
Compute the number of words that can be formed by rearranging the letters of "wapana" so that the a's are "evenly spaced". (The a's are evenly spaced if the number of letters (yes, this can include zero) between the�first a and the second a is the same as the number of letters between the second a an…
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If x and y are both whole numbers, what is the largest possible value of either x or y in the equation xy8x3y=0?
19. Off by ten?
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2. Minipop56: 765 points  One more to get the next lucky prime badge!
3. TimBluesWin: 655 points (1 achvmt pkg)
4. Imamadmad: 645 points (1 achvmt pkg)
5. Julianthewiki: …
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How many integers “n” in 1, 2, 3, … 50 are there such that, for all whole numbers “m”, “m!” never ends in exactly “n” zeros?
21.
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2. Minipop56: 765 points  One more to get the next lucky prime badge!
3. TimBluesWin: 655 points (1 achvmt pkg)
4. Imamadmad: 645 points (1 achvmt pkg)
5. Julianthewiki: 425…
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Solve question F.
Minipop, congrats!
1. Blueeighthnote: 13415 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 765 points  One more to get the next lucky prime badge!
3. TimBluesWin: 655 points (1 achvmt pkg)
4. Imamadmad: 645 points (1 achvmt pkg)
5. Julianthewiki: 425 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...: 230 points (1 achvmt pkg)
7. …
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Achievements earned during the last question: 0
Solve question E.
Blueeighthnote, congrats!
1. Blueeighthnote: 13415 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. Minipop56: 755 points  One more to get the next lucky prime badge!
3. TimBluesWin: 655 points (1 achvmt pkg)
4. Imamadmad: 645 points (1 achvmt pkg)
5. Julianthewiki: 425 points (1 achvmt pkg)  RETIRED
6. Wikia Contributor 69.235...: 230 points (1 achvmt …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 1
MINIPOP56 EARNS THE FIRST DURATION BADGE!
4Leaf Clover! (+100 points)  Awarded for participating on the Question of the Day everyday during the month of March!
Kristin and Benjamin own a cycle shop. They sell bicycles and tricycles. On Tuesday, they got a new shipment of cycles that needed to be assembled. In the shipment, there were 28 seats and 67 wheels. How many tricycles needing …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
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Achievements earned during the last question: 0
I will leave this question open for two days as I updated this kind of late.
Today is Mr. 3primetime3's birthday! He now realizes that in 75 years, he will be exactly 6 times older than he is right now. How old was 3primetime3 15 days ago?
LUCKY PRIME HINT: The year in which 3primetime3 was born.
[None]
1. Blueeighthnote: 3210 points (2 achvmt pkgs)  One more to get the next lucky prime ba…
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
Lefty7788, your turn again to make the question!
LUCKY PRIME HINT: Lefty, you make this too!
The solution was 97, and the lucky prime was 3. Using the same rule, we can find that there were three dots in that sentence.
1. Blueeighthnote: 3210 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4.…
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
Math Competition Question!
In 8 years, Denny will be 3 times the age that Polly was last year. 25 years ago, their ages added to 83. How old is Denny now?
LUCKY PRIME HINT: GUESS AGAIN!
The solution was 202, and the lucky prime was 11.
1. Blueeighthnote: 3210 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
No one answered the actual QOTD (just posted the answers), so I will keep the same question open for one more day.
Define the operation ▲ as A▲B = AB + (A/B) for all integers A and B. What is the value of (6▲3)▲(4▲2)?
LUCKY PRIME HINT: The numbers of dots in this sentence.......
1. Blueeighthnote: 3190 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. TimBluesWin: 655 p…
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
Define the operation ▲ as A▲B = AB + (A/B) for all integers A and B. What is the value of (6▲3)▲(4▲2)?
LUCKY PRIME HINT: The numbers of dots in this sentence.......
Did you guys get it right? The lucky prime was 211.
1. Blueeighthnote: 3170 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4. …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
I'm gonna make this before something weird happens to my account again.
Blueeighthnote and Minipop, please make questions for today. Solve each other's questions!
LUCKY PRIME HINT: It has a 2.
Everyone got it right! The lucky prime was 3.
1. Blueeighthnote: 3170 points (2 achvmt pkgs)  One more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 poi…
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
I'm gonna make this before something weird happens to my account again.
At “Middle” Middle School, 12 students are in line for Picture Retake Day. Of the 12 students, 3 are 6th graders, 4 are 7th graders, and 5 are 8th graders. The photographer doesn’t care which student goes first, or which grade goes first, but he does insist that the kids are in line by grade so that all of one grade …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
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Achievements earned during the last question: 0
How many parentheses were in yesterday's question?
LUCKY PRIME: It has a 1 in this 3 digit number.
139. The lucky prime was 2. There were two days in a row without a hint!
1. Blueeighthnote: 3150 points (2 achvmt pkgs)  Two more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4. Minipop56: 545 points  Two more to get the n…
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
When the sum 3^6 + 9^3 +3 ^13 + 27^6 is written as the product of three consecutive integers, what is the middle of the three integers?
Emmaelise456, what was the answer? Who got it right?
1. Blueeighthnote: 3120 points (2 achvmt pkgs)  Two more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4. Minipop56: 510 points  Two …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
Emmaelise456, if you want to make the next question of the day/lucky prime, do so here.
DalekJames, if you want to make the next question of the day, do so here.
Minipop56, what was the answer?
1. Blueeighthnote: 3020 points (2 achvmt pkgs)  Three more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4. Minipop56: 510 points …
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Hey guys! I'm seeing a lot of new users! That's so great!
New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right.
For newcomers who are seeing this blog post for the first time, please read the rules to get started!
Achievements earned during the last question: 0
Minipop56, if you want to make the next question of the day/lucky prime, do so here.
The answer was 7/10.
1. Blueeighthnote: 3020 points (2 achvmt pkgs)  Three more to get the next lucky prime badge!
2. TimBluesWin: 655 points (1 achvmt pkg)
3. Imamadmad: 645 points (1 achvmt pkg)
4. Minipop56: 510 points  Three more to get the next lucky prime badge!
5. Julianthewiki: 395 points (1 achvmt pk…
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