tag:blogger.com,1999:blog-15628310.post116040066515330495..comments2021-01-21T13:53:28.761-05:00Comments on Question of the day: Seven Ate NineAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-15628310.post-1160488047017975832006-10-10T09:47:00.000-04:002006-10-10T09:47:00.000-04:00I'm afraid I have a very simple answer to this one...I'm afraid I have a very simple answer to this one. Note that 7x8x9 = 504. Divide 789,000 by 504 you get a remainder of 240. 540-240 = 264. So 789,264 is one of the possible numbers. The only other number divisible by 504 is 789,768, which repeats the 7 and 8 which were restricted.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1160481397442877992006-10-10T07:56:00.000-04:002006-10-10T07:56:00.000-04:00The explanations are skipping a lot of steps, I th...The explanations are skipping a lot of steps, I think. Mike--will you provide a full one?Andyhttps://www.blogger.com/profile/09479999070145487506noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1160405019742841262006-10-09T10:43:00.000-04:002006-10-09T10:43:00.000-04:00dang, you barely beat me to a similar explanation....dang, you barely beat me to a similar explanation. one addition to your explanation (which is pretty obvious maybe): the reason you need X+Y+Z=12 is so the total 7+8+9+X+Y+Z will be divisible by 9 and so will the whole number (since every number divisible by 9 has the sum of its digits divisible by 9 also). also, you know 1000 is divisible by 8, and so is 789,000, which is why you can just look at the last three digits for divisibility by 8.Abehttps://www.blogger.com/profile/04424868492071587450noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1160404656699266492006-10-09T10:37:00.000-04:002006-10-09T10:37:00.000-04:00Not so tough, I don't think.X+Y+Z = 3 or 12 or 21,...Not so tough, I don't think.<BR/><BR/>X+Y+Z = 3 or 12 or 21, but 21 is too high (requires a 7, 8 or 9).<BR/><BR/>If X + Y + Z = 3, then we have something with three 1's, but that is no good for divisibility by 8, or a 0, a 1, and a 2, but numbers ending in 012 are not divisible by 8 either and 789,120 is not divisible by 7. Therefore X+Y+Z = 12.<BR/><BR/>Choose from the following list:<BR/>660, 651, 642, 633, 552, 543, 444.<BR/><BR/>The arrangements that are divisible by 8 are: 264, 336, 552 and 624. <BR/><BR/>789 - 264 = 525, bingo<BR/>789 - 336 = 453, not divisible by 7.<BR/>789 - 552 = 237, not divisible by 7.<BR/>789 - 624 = 165, not divisible by 7.<BR/><BR/>So, 789,264 =<BR/>9*87,696 =<BR/>8*98,658 =<BR/>7*112,752Anonymousnoreply@blogger.com