C1ay Posted April 8, 2005 Report Share Posted April 8, 2005 FishTeacher's thread on palindromes gave me an idea for some new number puzzles. Can you extend these sequences? 3, 5, 7, 9, 15, 17,.....4, 8, 10, 13, 16, 20,....5, 10, 15, 17, 21, 25,....6, 12, 18, 24, 26, 31,..... and a sort of related sequence the other sequences lead too, 1, 5, 27, 194,.... Now I think I have said too much already ;) Quote Link to comment Share on other sites More sharing options...
tom Posted April 8, 2005 Report Share Posted April 8, 2005 212329361865 Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 8, 2005 Author Report Share Posted April 8, 2005 212329361865 Very good, I'm impressed ;) Quote Link to comment Share on other sites More sharing options...
tom Posted April 9, 2005 Report Share Posted April 9, 2005 The first series are base 2 palindromes the second base 3 , ... . The last is special 1 is 1 in base 2 , 5 is 12 in base 3 , 27 is 123 in base 4, 194 is 1234 in base 5, ...We could transform this into a game. Somebody askes a question the first person who answers correct will ask the next question. If you see that in the last 24 hours there wasn't any post you will ask the next question, if there was one ( even a false response ) the first poster will answer the question and the author should give the solution to his question.PS The questions should be math or physics related and not google questions. Here is my question: You have 12 coins. One of them has a different mass ( and you don't know if it is smaller or greater than the rest). Useing a balance and 3 measurements you must determine the coin and if it's lighter or heavier than the other 11 coins. This is a math question so please don't give a physics solution . ;) Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 9, 2005 Author Report Share Posted April 9, 2005 The first series are base 2 palindromes the second base 3 , ... . The last is special 1 is 1 in base 2 , 5 is 12 in base 3 , 27 is 123 in base 4, 194 is 1234 in base 5, ...We could transform this into a game. Somebody askes a question the first person who answers correct will ask the next question. If you see that in the last 24 hours there wasn't any post you will ask the next question, if there was one ( even a false response ) the first poster will answer the question and the author should give the solution to his question.PS The questions should be math or physics related and not google questions. Here is my question: You have 12 coins. One of them has a different mass ( and you don't know if it is smaller or greater than the rest). Useing a balance and 3 measurements you must determine the coin and if it's lighter or heavier than the other 11 coins. This is a math question so please don't give a physics solution . ;)Of course, with the answers to the solution hidden others may continue working on the original problem. Although they now have the next number in the sequence they still have the puzzle of finding the next one after yours ;) I don't know that it would be fair for me to answer the 12 coin problem since it is quite an old problem I've faced before. Perhaps I'll wait aq day or two and post a hint. Speaking of hints, there is a hint to my sequences in every post I make ;) Quote Link to comment Share on other sites More sharing options...
tom Posted April 9, 2005 Report Share Posted April 9, 2005 Thanks for the edit. I didn't have time to look through the source of the page to find the color so I've selected the nearest color in the list. Another rule. When you post your solution , post it like this *color=#F6F8FA] solution */color] ( use [ instead of * ) , so that other users can solve the problems if they want without unwillingly seeing the solution. Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 10, 2005 Author Report Share Posted April 10, 2005 Hum, there doesn't seem to be any guesses to either problem. Maybe it would help to begin each sequence as 11...Start the 12 coin problem by weighing coins 1,2,3,4 against 5,6,7,8. Quote Link to comment Share on other sites More sharing options...
Fishteacher73 Posted April 12, 2005 Report Share Posted April 12, 2005 Split and weigh....6 vs. 6Take the light stack, 3 vs. 3Take the light stack and weigh 1vs 1.If on is lighter it is false, if they balance the one left out is fake. Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 12, 2005 Author Report Share Posted April 12, 2005 Split and weigh....6 vs. 6Take the light stack, 3 vs. 3Take the light stack and weigh 1vs 1.If on is lighter it is false, if they balance the one left out is fake.But you don't know if the counterfeit coin is heavier or lighter, only that it is different. Quote Link to comment Share on other sites More sharing options...
Dark Mind Posted April 12, 2005 Report Share Posted April 12, 2005 Nice, I like the hints. I've recently seen this problem too though, so it would be unfair for me to answer (It was a bonus question on a recent physics test). Quote Link to comment Share on other sites More sharing options...
C1ay Posted April 12, 2005 Author Report Share Posted April 12, 2005 Nice, I like the hints. I've recently seen this problem too though, so it would be unfair for me to answer (It was a bonus question on a recent physics test).Divide the coins into 3 groups of 4 and number them 1 - 12, not groups of 6So, contribute a hint then :xx: Quote Link to comment Share on other sites More sharing options...
tom Posted April 13, 2005 Report Share Posted April 13, 2005 or you could name them after the way they influence the balance if they go up name them U coins , in they go down D coins, coins that you know they are ok G coins and suspect coins S. First there are 12 S and then ... Quote Link to comment Share on other sites More sharing options...
Dark Mind Posted April 13, 2005 Report Share Posted April 13, 2005 Divide the coins into 3 groups of 4 and number them 1 - 12, not groups of 6So, contribute a hint then :xx: Uhh, okay. After dividing them into groups of three weigh group one against group two, there are now two possibilities: 1) They weigh the same and the "right" coin is in the 9,10,11,12 group and problem solved from there on out easily enough) or 2) They don't balance and then... Quote Link to comment Share on other sites More sharing options...
Aki Posted April 14, 2005 Report Share Posted April 14, 2005 What was the solution to the original number sequence question? I can't get them Quote Link to comment Share on other sites More sharing options...
tom Posted April 14, 2005 Report Share Posted April 14, 2005 The first series. Write the numbers there in base 2 and the second series write it in base 3 . You should observe something :xx: Quote Link to comment Share on other sites More sharing options...
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