This is the 9 digit problem: Arrange the digits one through nine to form a nine-digit in such a way that the number formed by any two consecutive digits is the product of two single digit numbers.
2006-12-03 04:23:27 · 3 answers · asked by crystalblue129 2 in Science & Mathematics ➔ Mathematics
Well, I saw fairly quickly that the 9 had to go last, since there are no 9x numbers that are the product of two single digit numbers. Then I saw the 4 had to be in front of the 9, since 49 is the only x9 number that is the product of two single digit numbers.
Next, I saw that the only two numbers with 7 that work are 72 and 27. So, with the last spot already taken by the 9, that means the 7 has to go in the first spot and the 2 in the second spot. (The number can't start 27, of course, because the 2 can't be used again.)
Working with the 8 now...The 8 can't be first or last, since those spots are taken, so we need an 8x number. For this, the only number that works is 81.
So far we have 72xxxxx49, and we also know 81 must follow in sequence somewhere. The number after the 2 can't be 1, and it also can't be 3 or 6, leaving 5 or 8 as the two possibilities for the third digit. When I try 5, however, I find the digit after that has to be 6, and the digit after the 6 has to be 3... and then I hit a dead end. So, 5 doesn't work as the third digit - it has to be 8.
So now we have 7281xxx49. The 3 can't go to the right of the 1 or to the left of the 4, so it must be the middle unknown digit. We have 7281x3x49. With only the 5 and 6 left, we test those two and see the only answer is: 728163549.
Interesting problem, actually. Wow, two posters figured this out in under 10 minutes? Those guys must be frickin' geniuses.
2006-12-03 05:25:03 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The number is 728163549. How to get this? Well I knew 9 must go at the end because no number in the 90s can be the product of 2 single digit numbers. The only two digit number ending in nine that works is 4, so I knew the last 2 were 49. Next, I know that the only number that can go after 7 is a 2 and after 8 is a 1. I then knew 7 must be the first number because no number can end in a 7 and be the product of 2 single digit numbers (except 27, but the 2 must go after the 7). I just kind of fit the rest of the numbers inbetween.
2006-12-03 04:41:49 · answer #2 · answered by Michael W 2 · 1⤊ 0⤋
728163549
2006-12-03 04:39:18 · answer #3 · answered by Amy F 5 · 0⤊ 0⤋