tag:blogger.com,1999:blog-5730391.post718012289464021062..comments2024-03-29T04:50:38.638-07:00Comments on Blaine's Puzzle Blog: Use the digits 1 through 9 exactly once...Blainehttp://www.blogger.com/profile/06379274325110866036noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5730391.post-80229991344818228982008-05-16T08:56:00.000-07:002008-05-16T08:56:00.000-07:00Compute 10² through 31². That will give you all th...Compute 10² through 31². That will give you all the 3-digit perfect squares. Now eliminate any with repeated digits within them. Also, several of them use the same set of digits, so I’ve grouped them together. That leaves 10 groups of squares.<BR/>169, 196, 961<BR/>256, 625<BR/>289<BR/>324<BR/>361<BR/>529<BR/>576<BR/>729<BR/>784<BR/>841<BR/><BR/>There are only two that contain the digit 3 (324 and 361), so let’s work with them.<BR/><BR/>If you pick 324, you can eliminate squares with those digits: That leaves:<BR/>169, 196, 961<BR/>576<BR/>But there is no square with an 8 left, so this won’t.<BR/><BR/>We know that 361 will be one of the squares. You can eliminate squares with those digits: That leaves:<BR/>289<BR/>529<BR/>729<BR/>784<BR/><BR/>You need a 4, so 784 will be one of the squares.<BR/>You need a 5, so 529 will be one of the squares.<BR/><BR/>Checking you see that all the digits appear exactly once in these 3 squares:<BR/><BR/>Answer:<BR/>361, 529 and 784<BR/>(which are 19², 23² and 28²)Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-40977910383259435482008-02-25T09:47:00.000-08:002008-02-25T09:47:00.000-08:00I had a tough time understanding what the clue mea...I had a tough time understanding what the clue meant. Now that I have seen Eric's response, it makes perfect sense. I didn't have the time to ask, but will endeavor to do so next time. Thanks, this was a clever one!Don Hodunhttps://www.blogger.com/profile/10629317119387671011noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-41080497783797150832008-02-24T12:03:00.000-08:002008-02-24T12:03:00.000-08:00The squares of the numbers between 10 and 31 are t...The squares of the numbers between 10 and 31 are the only 3-digit ones, and eliminating those with repeated digits leaves only 13 choices (of which 169, 196, and 961 are equivalent). <BR/>A little playing around led to <BR/>361, 529, 784.EricMargelhttps://www.blogger.com/profile/02090556952649043090noreply@blogger.com