tag:blogger.com,1999:blog-15628310.post8710103835766198797..comments2021-03-02T05:02:26.838-05:00Comments on Question of the day: Change, mister?Anonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-15628310.post-36250698628698434832007-03-16T08:32:00.000-04:002007-03-16T08:32:00.000-04:00Mr Don, that last sentence was in the way of a hin...Mr Don, that last sentence was in the way of a hint. I was looking for the smallest number of coins that you can have such that you can't make a dollar in change. One dollar = one dollar coin is valid, since one dollar coin is change.<BR/><BR/>jonathan, I believe that's a very thorough answer and I can't add anything else to it.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-13592139329454568712007-03-15T21:47:00.000-04:002007-03-15T21:47:00.000-04:00Certainly 101 cannot be done. But can we find smal...Certainly 101 cannot be done. But can we find smaller? <BR/><BR/>1 - 4 are easy (quarters, dollars, and halfs). <BR/><BR/>HQDDN is 5, HDDDDD is 6, and we cover up to 11 by exchanging dimes for nickels 1 for 2. <BR/><BR/>Then 10D is good, and with the same exchange, 20 is covered. <BR/><BR/>3D5P can swap for 7N, bringing us from 20N to 6D6N10P for 22. <BR/><BR/>Swapping those 6D one at a time for 2N each gets us to 18N10P (28). <BR/><BR/>The 3D5P/7N swap brings us up to 6D4N20P (30). <BR/><BR/>D/2N shifts us to 16N20P (36). <BR/><BR/>3D5P/7N brings us back to 6D2N30P (38). <BR/><BR/>D/2N gets back to 14N30P (see the problems looming?)<BR/><BR/>3D5P/7N brings us back to 6D40P (46). <BR/><BR/>D/2N --> 12N40P (52)<BR/><BR/>3D5P/7N can be applied once: 3D5N45P (53). <BR/><BR/>D/2N --> 11N45P (56)<BR/><BR/>3D5P/7N --> 3D4N50P (57). <BR/><BR/>D/2N --> 10N50P (60)<BR/><BR/>3D5P/7N --> 3D3N55P (61). <BR/><BR/>D/2N --> 9N55P (64)<BR/><BR/>3D5P/7N --> 3D2N60P (65). <BR/><BR/>D/2N --> 8N60P (68)<BR/><BR/>3D5P/7N --> 3D1N65P (69). <BR/><BR/>D/2N --> 7N65P (72)<BR/><BR/>3D5P/7N --> 3D70P (73). <BR/><BR/>D/2N --> 6N70P (76)<BR/><BR/>Q75P is also (76)<BR/><BR/>2DN75P works, but that's (78).<BR/><BR/>That would make it 77Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-46384079889459962552007-03-15T18:26:00.000-04:002007-03-15T18:26:00.000-04:00This is a little confusing. The smallest number o...This is a little confusing. The smallest number of coins that I can have without being able to make change for a dollar is 1 - the dollar coin.<BR/><BR/>However, based on the last sentence, "it's lower than 100", are you asking for the highest number of coins?<BR/><BR/>If so, wouldn't it be 99 pennies?Mr. Donhttps://www.blogger.com/profile/03794433688939455277noreply@blogger.com