I am 5 digits long...
From: Anonymous Date: Fri, 16 Dec 94 10:43:05 EST Subject: Math Problem Hello This is Mario Ceste and Jeff Larioni from Floris Elem. School in Herndon, Virginia. Our Problem is this I am 5 digits long I am divisible by 3 and 9, but not 6 My digits add up to 27 When my first and last digits are added, you will get a multiple of seven. My lowest digit is 3 If you add up my second and fourth digits, you get 10 No number is used more than once On the left of the comma, the numbers from left to right decrease by 1. On the right of the comma, the numbers increase by 3.
Date: Fri, 16 Dec 1994 11:40:41 -0500 (EST) From: Dr. Sydney Subject: Re: Math Problem Hello Mario and Jeff! Thanks for writing Dr. Math. This is quite a big word problem -- pretty tricky. Let's see... I'll tell you how I approached it, though there are many different ways of doing a problem like this one. Since the lowest digit is three and the numbers to the right of the comma increase by three and the numbers to the left of the comma decrease by one, the three must either be the digit in the thousands place or the digit in the hundreds place, right? So, we can check both possibilities: If the three is in the thousands place, there must be a 7 in the tens place, since the digits in the thousands place and the tens place must add up to 10. But that is impossible, since the digit in the ones place is supposed to be 3 more than the digit in the tens place -- if 7 is in the tens place, then that would mean 10 is in the ones place, but we can't have a two digit number in the ones place. So, the three must not in the thousands place. Consider the other possibility (and we'll hope it works!). If the three is in the hundreds place, then we have a 6 in the tens place and a 9 in the ones place. Since there is a 6 in the tens place, and the digits in the tens place and the thousands place have to add up to 10, there must be a 4 in the thousands place. This means that the ten thousands place must have a 5 (one bigger than 4). So, our number is this: 54,369 Now, check all of the properties. Do the digits add up to 27? Is this number divisible by 9 and 3 but not 6? etc. I think you'll find this number works! So, there you have it. If you have any other questions, please write back. --Sydney P.S. We are so busy answering students' questions that we usually don't take questions like this that are more of a puzzle than anything else, so if you write back, try not to ask any "puzzle" questions. If puzzles are what interest you (which is Great!--they can be lots of fun) you might want to subscribe to the newsgroup rec.puzzles on the internet. Have fun with it!
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