tag:blogger.com,1999:blog-15628310.post2500123591566412550..comments2021-01-21T13:53:28.761-05:00Comments on Question of the day: Pocket ChangeAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-15628310.post-83680271949122791552007-03-17T15:01:00.000-04:002007-03-17T15:01:00.000-04:00Jonathan, I have looked at them from time to time....Jonathan, I have looked at them from time to time. I like your recent puzzle on black and white marbles and thought about creating a variant here. But, what with time limits, I just haven't gotten a chance.<BR/><BR/>I really appreciate the encouragement, thanks.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-61981193616756590832007-03-17T12:15:00.000-04:002007-03-17T12:15:00.000-04:00Mike,you come up with these every day? I know I di...Mike,<BR/><BR/>you come up with these every day? I know I disappear for weeks on end (rhythms of life and teaching). I am happy when I have a nice solution with a reasonable explanation.<BR/><BR/>But you do this every day. Credit where credit is due. No way could I do this.<BR/><BR/>Btw, have you looked at my (far less frequent) puzzles?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-23059230563719273422007-03-16T08:30:00.000-04:002007-03-16T08:30:00.000-04:00jonathan, there are some days when I think I shoul...jonathan, there are some days when I think I shouldn't be the one running this. Seeing your answer makes me think that way.<BR/><BR/>Nick, the idea for this question was to figure out how many coins you needed in your pocket so that there are six ways (and only six ways) of making one dollar. Four quarters make up a dollar, but there is no other combination of four that makes up a dollar.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-53427976525022778972007-03-15T20:56:00.000-04:002007-03-15T20:56:00.000-04:00But how do you like nickels/3 has a remainder of 1...But how do you like nickels/3 has a remainder of 1 detail? 1, 4, 7, 10 or 13.<BR/><BR/>One idea here is that we are trading coins such that we have equal numbers and equal values. How can we do that?<BR/><BR/>4D = 1Q3N<BR/>1Q5P = 6N<BR/>------------<BR/>1Q4D5P = 1Q9N<BR/>-1Q -1Q<BR/>------------<BR/>4D5P = 9N<BR/><BR/>So the first two lines can be combined to create the last. We just need enough coins to apply this 5 times.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-45943200221019415472007-03-15T18:52:00.000-04:002007-03-15T18:52:00.000-04:00maybe im missing somthing? but four quarters make ...maybe im missing somthing? but four quarters make a dollar, ten dimes make a dollar, twenty nickels make a dollar, and one hundred pennies make a dollar. thats all common knowledge, but none of the above use fifteen coins, and adding to the above combinations, that makes ten different combinations?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-32745398280909698072007-03-15T09:21:00.000-04:002007-03-15T09:21:00.000-04:00That's right Jonathan. You need 15 coins.Since th...That's right Jonathan. You need 15 coins.<BR/>Since there are no half dollars, you can use quarters, dimes, nickels and pennies. The six ways you can do this are:<BR/>__Q D N P<BR/>1)3 1 1 10<BR/>2)2 1 7 5<BR/>3)1 1 13 0<BR/>4)1 5 4 5<BR/>5)0 9 1 5<BR/>6)0 5 10 0<BR/><BR/>And this is a unique answer, although I'll leave the proof to you ;-)Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-34738822270120254302007-03-15T07:46:00.000-04:002007-03-15T07:46:00.000-04:00Oops! I mixed up the words "nickels" and "dimes" a...Oops! I mixed up the words "nickels" and "dimes" above. All else is good.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-61521123647753515272007-03-15T07:44:00.000-04:002007-03-15T07:44:00.000-04:00It looks like, when you divide the number of nicke...It looks like, when you divide the number of nickels by 3, the remainder is 1. That's interesting. Five nickels and ten dimes makes a dollar, and there are five more ways with the same number of coins (as long as half dollars are excluded)Anonymousnoreply@blogger.com