#WarmUp
Two drivers started at the same time, covered the same distance, and returned home at the same time. But one rode twice as long as the other rested on his trip, and the other rode three times as long as the first one rested on his trip. Who rode faster?
Two drivers started at the same time, covered the same distance, and returned home at the same time. But one rode twice as long as the other rested on his trip, and the other rode three times as long as the first one rested on his trip. Who rode faster?
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#FAQ
Q: How are points awarded (withdrawn) for answers?
A: When the moderator has checked your answer and counted it, you are awarded the number of points that stands in the weight of the task. The weight of the task may change, then the rating will be recalculated automatically.
Q: How are points awarded (withdrawn) for answers?
A: When the moderator has checked your answer and counted it, you are awarded the number of points that stands in the weight of the task. The weight of the task may change, then the rating will be recalculated automatically.
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Weighing #Puzzle by cerebrate.it
8 coins:
You have 8 coins that appear to be identical, except one (which is counterfeit) is slightly heavier than the others. What is the minimal number of weighings on the balance scale that is required to find the counterfeit coin?
8 coins:
You have 8 coins that appear to be identical, except one (which is counterfeit) is slightly heavier than the others. What is the minimal number of weighings on the balance scale that is required to find the counterfeit coin?
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#AroundTheMath
Did you know that...
A) 'four' is the only number in the English language that is spelt with the same number of letters as the number itself.
B) From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand").
Did you know that...
A) 'four' is the only number in the English language that is spelt with the same number of letters as the number itself.
B) From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand").
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#WarmUp
A nonstop train leaves Moscow for Leningrad at 60 miles per hour. Another nonstop train leaves Leningrad for Moscow at 40 miles an hour. How far apart are the trains 30 minutes before they pass each other?
A nonstop train leaves Moscow for Leningrad at 60 miles per hour. Another nonstop train leaves Leningrad for Moscow at 40 miles an hour. How far apart are the trains 30 minutes before they pass each other?
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#FAQ
Q: What does the puzzle weight mean?
A: Puzzle weight - how much the user's rating will increase after successfully solving the problem. More weight is a more difficult puzzle.
The weight of the puzzle is determined by how often the puzzle is correctly answered, namely, by the ratio of the number of those who solved to the number of those who saw the puzzle. Like this:
100% >= weight 1 >= 8% > weight 2 >= 4% > weight 3 >= 2% > weight 4>= 1% > weight 5 >= 0%.
At the same time, everyone who visited the site after the publication of the puzzle is considered to have seen the puzzle.
A weight of 0 means that the puzzle is out of the rating, this is possible in two cases: a) if special knowledge is needed to solve the problem; b) you just need to guess the answer.
Non-zero problems are published with an initial weight of 1.
Puzzle weights are recalculated periodically (about once a month) (at this point, player ratings can change both positively and negatively).
Q: What does the puzzle weight mean?
A: Puzzle weight - how much the user's rating will increase after successfully solving the problem. More weight is a more difficult puzzle.
The weight of the puzzle is determined by how often the puzzle is correctly answered, namely, by the ratio of the number of those who solved to the number of those who saw the puzzle. Like this:
100% >= weight 1 >= 8% > weight 2 >= 4% > weight 3 >= 2% > weight 4>= 1% > weight 5 >= 0%.
At the same time, everyone who visited the site after the publication of the puzzle is considered to have seen the puzzle.
A weight of 0 means that the puzzle is out of the rating, this is possible in two cases: a) if special knowledge is needed to solve the problem; b) you just need to guess the answer.
Non-zero problems are published with an initial weight of 1.
Puzzle weights are recalculated periodically (about once a month) (at this point, player ratings can change both positively and negatively).
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#AboutUs – Puzzle answering rules
1. Please write your answer on the first line. And then the justification. This way moderator can understand a complex solution more easily.
2. Try to formulate your solution in a structured and detailed manner. Difficult-to-understand solutions are checked much more slowly.
3. The moderator in the process of the solution review can clarify the condition and ask various questions.
4. The answer to the problem must always be justified. Moreover, so that another person, the moderator, could easily verify the correctness of the justification and the result. The exceptions are riddles and puzzles on pattern recognition, as well as the puzzles where it is explicitly written that justification is not required.
5. The so-called "original answers" are not the standards by which the moderators check the answers, with the exception of riddles.
6. If you are asked to justify some statement, to clarify the «obvious», this is not because the moderators are stupid, but because the «obvious» is most often incorrect or there are a lot of incorrect justifications for it.
7. Please check and reconsider your answer before sending.
8. Apologizing for incorrect solution, writing that I was wrong, I will think ... and so on is not worth it. These posts will only bother moderator, since they need to review them as well.
1. Please write your answer on the first line. And then the justification. This way moderator can understand a complex solution more easily.
2. Try to formulate your solution in a structured and detailed manner. Difficult-to-understand solutions are checked much more slowly.
3. The moderator in the process of the solution review can clarify the condition and ask various questions.
4. The answer to the problem must always be justified. Moreover, so that another person, the moderator, could easily verify the correctness of the justification and the result. The exceptions are riddles and puzzles on pattern recognition, as well as the puzzles where it is explicitly written that justification is not required.
5. The so-called "original answers" are not the standards by which the moderators check the answers, with the exception of riddles.
6. If you are asked to justify some statement, to clarify the «obvious», this is not because the moderators are stupid, but because the «obvious» is most often incorrect or there are a lot of incorrect justifications for it.
7. Please check and reconsider your answer before sending.
8. Apologizing for incorrect solution, writing that I was wrong, I will think ... and so on is not worth it. These posts will only bother moderator, since they need to review them as well.
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#WarmUp
Each morning Boris walks to school. At one-fourth of the way he passes the machine and tractor station; at one-third of the way, the railroad station. At the machine and tractor station its clock shows 7:30, and at the railroad station its clock shows 7:35. When does Boris leave his house, when does he reach school?
Each morning Boris walks to school. At one-fourth of the way he passes the machine and tractor station; at one-third of the way, the railroad station. At the machine and tractor station its clock shows 7:30, and at the railroad station its clock shows 7:35. When does Boris leave his house, when does he reach school?
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#FAQ
Q: What does the task rating mean?
A: At the moment - the sum of the ratings that users voted for. A kind of "arguing audience award".
Q: What does the task rating mean?
A: At the moment - the sum of the ratings that users voted for. A kind of "arguing audience award".
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#FAQ
Q: What does the task rating mean?
A: At the moment - the sum of the ratings that users voted for. A kind of "arguing audience award".
Q: What does the task rating mean?
A: At the moment - the sum of the ratings that users voted for. A kind of "arguing audience award".
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#WarmUp
Given two numbers, if we subtract half the smaller number from each number, the result with the larger number is three times as large as the result with the smaller number. How many times is the larger number as large as the smaller number?
Given two numbers, if we subtract half the smaller number from each number, the result with the larger number is three times as large as the result with the smaller number. How many times is the larger number as large as the smaller number?
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Knights, Knaves and Jokers #Puzzle by cerebrate.it
A circle of lies:
After a shipwreck, a Megamind found himself on an island where some natives always lie and some always tell the truth. As a ritual, all natives stood in a circle facing the center, joined their hands and everybody told the Megamind whether his right hand side neighbor is a liar or a truth-teller. Based on this information, the Megamind was able to determine the exact percentage of natives that tell the truth. Can you also determine this percentage?
A circle of lies:
After a shipwreck, a Megamind found himself on an island where some natives always lie and some always tell the truth. As a ritual, all natives stood in a circle facing the center, joined their hands and everybody told the Megamind whether his right hand side neighbor is a liar or a truth-teller. Based on this information, the Megamind was able to determine the exact percentage of natives that tell the truth. Can you also determine this percentage?
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#AroundTheMath
Have you heard about Fermat's theorem? No?! Then let's study it in order.
Once the French lawyer Pierre de Fermat became interested in mathematics - he began to study many books on mathematics, but most of all he was interested in the book of Diophantus of Alexandria "Arithmetic". While studying the book, he introduced his arguments into it, the main of which was the addition to the Pythagorean formula x²+y²=z². Fermat decided to replace the powers of 2 with an unknown number n, turning the formula into xⁿ+yⁿ=zⁿ. Immediately he realized that there was no solution to this formula, and it could be proved. He was even able to come up with a proof, but there was not enough room in the book for such a large proof...
That's how appeared the theorem, which took ~350 years to prove!
Have you heard about Fermat's theorem? No?! Then let's study it in order.
Once the French lawyer Pierre de Fermat became interested in mathematics - he began to study many books on mathematics, but most of all he was interested in the book of Diophantus of Alexandria "Arithmetic". While studying the book, he introduced his arguments into it, the main of which was the addition to the Pythagorean formula x²+y²=z². Fermat decided to replace the powers of 2 with an unknown number n, turning the formula into xⁿ+yⁿ=zⁿ. Immediately he realized that there was no solution to this formula, and it could be proved. He was even able to come up with a proof, but there was not enough room in the book for such a large proof...
That's how appeared the theorem, which took ~350 years to prove!
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#FAQ
Q: What does the user rating mean?
A: The user's rating is the sum of the weights of the credited tasks. The higher the rating, the more tasks the user has already solved.
Q: What does the user rating mean?
A: The user's rating is the sum of the weights of the credited tasks. The higher the rating, the more tasks the user has already solved.
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#WarmUp
You pick up 1 through 6 of 30 matches. The second player picks up 1 through 6 matches, and so on. The player who picks up the last match wins. How do you get to pick up the last match?
You pick up 1 through 6 of 30 matches. The second player picks up 1 through 6 matches, and so on. The player who picks up the last match wins. How do you get to pick up the last match?
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#Games #Puzzle by Cerebrate.it
Tic-tac-toe, the Megaminds style:
Two Megaminds decided to play tic-tac-toe using new rules. They use a regular 3x3 playing pad, but each player can choose to place either an X or an O into one of the cells. The winner is still the one who arranges three X's or three O's in a line. Is there a winning strategy in this game? Which player has it?
Tic-tac-toe, the Megaminds style:
Two Megaminds decided to play tic-tac-toe using new rules. They use a regular 3x3 playing pad, but each player can choose to place either an X or an O into one of the cells. The winner is still the one who arranges three X's or three O's in a line. Is there a winning strategy in this game? Which player has it?
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#FAQ
Q: How does a user change their rating?
A: Task weight - how much the user's rating will increase after successfully solving the problem. More weight is a more difficult task.
Q: How does a user change their rating?
A: Task weight - how much the user's rating will increase after successfully solving the problem. More weight is a more difficult task.
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#WarmUp
How many minutes is it until six o'clock if fifty minutes ago it was four times as many minutes past three o'clock?
How many minutes is it until six o'clock if fifty minutes ago it was four times as many minutes past three o'clock?
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#FAQ
Q: What do the numbers in the TOP lists mean to the right of the names?
A: The rating of users included in this TOP-10.
Q: What do the numbers in the TOP lists mean to the right of the names?
A: The rating of users included in this TOP-10.
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For children #Puzzle by cerebrate.it
Five days:
Can you describe five consecutive days without referring to weekdays or days of the month?
Five days:
Can you describe five consecutive days without referring to weekdays or days of the month?
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