RE: [RollTideFan] Off season - again...
U R a Gene-E-us! -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Jeff Todd Sent: Thursday, April 29, 2004 9:41 PM To: RollTideFan-The University of Alabama Athletics Discussion List Subject: Re: [RollTideFan] Off season - again... Devo, Every positive integer is a multiple of 9 plus the sum of its digits. Here is why. Take 7843. That's equal to 7×1000 + 8×100 + 4×10 + 3 which equals 7×(999 + 1) + 8×(99 + 1) + 4×(9 + 1) + 3 which equals 7×999 + 7×1 + 8×99 + 8×1 + 4×9 + 4×1 + 3 which equals 7×999 + 7 + 8×99 + 8 + 4×9 + 4 + 3 which equals (7×999 + 8×99 + 4×9) + (7 + 8 + 4 + 3) which equals 9(7×111 + 8×11 + 4) + (7 + 8 + 4 + 3) which equals a multiple of 9 + the sum of the digits. Now when the number is rearranged, that number too is a multiple of 9 plus the sum of its digits. Since the sum of the digits is the same no matter how the digits are rearranged, when you subtract you get a multiple of 9 because the sum of the digits cancel and leave the difference of two multiples of 9, which is a multiple of 9. Since the result must be a multiple of 9, the sum of its digits must also be a multiple of 9. Now you are given all the digits but one, so you add all the digits but one, and that missing digit must be just enough to add to the sum of the other digits to make a multiple of 9. 7843 = multiple of 9 + (7+8+4+3) 4387 = multiple of 9 + (4+7+8+3) --- subtract these 3456 = multiple of 9 - multiple of 9 + (7+8+4+3) - (4+7+8+3) = a multiple of 9 + 0 = a multiple of 9 That multiple of 9 is also a multiple of 9 plus the sum of its digits. Therefore the sum of its digits must also be a multiple of 9. Suppose the person circles the 5 and gives you the three digits sqrambled as 4,6,3. You know the sum of the digits must be a multiple of 9. You add 4+6+3 and get 13. The next multiple of 9 is 18, so you know the circled digit must be 18-13 or 5. Gimme a dollar and I'll tell you how I figured that out. Gimme an extra dollar and I'll tell you how long it took me. Slef E. (The *E* stands for arithmagician) - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 10:02 AM Subject: [RollTideFan] Off season - again... Everyone has to try thisI am now in the phase where I am trying to figure it out http://digicc.com/fido/ DevO __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
Re: [RollTideFan] Off season - again...
Ewe da man Slef. Reading that just gave me a headache. LOL Joe The study of history is a powerful antidote to contemporary arrogance. It is humbling to discover how many of our glib assumptions, which seem to us novel and plausible, have been tested before, not once but many times and in innumerable guises; and discovered to be, at great human cost, wholly false. --Paul Johnson - Original Message - From: Jeff Todd [EMAIL PROTECTED] To: RollTideFan-The University of Alabama Athletics Discussion List [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 10:41 PM Subject: Re: [RollTideFan] Off season - again... Devo, Every positive integer is a multiple of 9 plus the sum of its digits. Here is why. Take 7843. That's equal to 7×1000 + 8×100 + 4×10 + 3 which equals 7×(999 + 1) + 8×(99 + 1) + 4×(9 + 1) + 3 which equals 7×999 + 7×1 + 8×99 + 8×1 + 4×9 + 4×1 + 3 which equals 7×999 + 7 + 8×99 + 8 + 4×9 + 4 + 3 which equals (7×999 + 8×99 + 4×9) + (7 + 8 + 4 + 3) which equals 9(7×111 + 8×11 + 4) + (7 + 8 + 4 + 3) which equals a multiple of 9 + the sum of the digits. Now when the number is rearranged, that number too is a multiple of 9 plus the sum of its digits. Since the sum of the digits is the same no matter how the digits are rearranged, when you subtract you get a multiple of 9 because the sum of the digits cancel and leave the difference of two multiples of 9, which is a multiple of 9. Since the result must be a multiple of 9, the sum of its digits must also be a multiple of 9. Now you are given all the digits but one, so you add all the digits but one, and that missing digit must be just enough to add to the sum of the other digits to make a multiple of 9. 7843 = multiple of 9 + (7+8+4+3) 4387 = multiple of 9 + (4+7+8+3) --- subtract these 3456 = multiple of 9 - multiple of 9 + (7+8+4+3) - (4+7+8+3) = a multiple of 9 + 0 = a multiple of 9 That multiple of 9 is also a multiple of 9 plus the sum of its digits. Therefore the sum of its digits must also be a multiple of 9. Suppose the person circles the 5 and gives you the three digits sqrambled as 4,6,3. You know the sum of the digits must be a multiple of 9. You add 4+6+3 and get 13. The next multiple of 9 is 18, so you know the circled digit must be 18-13 or 5. Gimme a dollar and I'll tell you how I figured that out. Gimme an extra dollar and I'll tell you how long it took me. Slef E. (The *E* stands for arithmagician) - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 10:02 AM Subject: [RollTideFan] Off season - again... Everyone has to try thisI am now in the phase where I am trying to figure it out http://digicc.com/fido/ DevO __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
Re: [RollTideFan] Off season - again...
Not really. I'm just tall enough to look over the smrat kids shoulders when we took tests. :-) And I'm a Google-Eyed Phool! http://tinyurl.com/2y6ok Stick with me, Devo. We'll go places, son! Slef E. - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Friday, April 30, 2004 8:01 AM Subject: RE: [RollTideFan] Off season - again... U R a Gene-E-us! -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Jeff Todd Sent: Thursday, April 29, 2004 9:41 PM To: RollTideFan-The University of Alabama Athletics Discussion List Subject: Re: [RollTideFan] Off season - again... Devo, Every positive integer is a multiple of 9 plus the sum of its digits. Here is why. Take 7843. That's equal to 7×1000 + 8×100 + 4×10 + 3 which equals 7×(999 + 1) + 8×(99 + 1) + 4×(9 + 1) + 3 which equals 7×999 + 7×1 + 8×99 + 8×1 + 4×9 + 4×1 + 3 which equals 7×999 + 7 + 8×99 + 8 + 4×9 + 4 + 3 which equals (7×999 + 8×99 + 4×9) + (7 + 8 + 4 + 3) which equals 9(7×111 + 8×11 + 4) + (7 + 8 + 4 + 3) which equals a multiple of 9 + the sum of the digits. Now when the number is rearranged, that number too is a multiple of 9 plus the sum of its digits. Since the sum of the digits is the same no matter how the digits are rearranged, when you subtract you get a multiple of 9 because the sum of the digits cancel and leave the difference of two multiples of 9, which is a multiple of 9. Since the result must be a multiple of 9, the sum of its digits must also be a multiple of 9. Now you are given all the digits but one, so you add all the digits but one, and that missing digit must be just enough to add to the sum of the other digits to make a multiple of 9. 7843 = multiple of 9 + (7+8+4+3) 4387 = multiple of 9 + (4+7+8+3) --- subtract these 3456 = multiple of 9 - multiple of 9 + (7+8+4+3) - (4+7+8+3) = a multiple of 9 + 0 = a multiple of 9 That multiple of 9 is also a multiple of 9 plus the sum of its digits. Therefore the sum of its digits must also be a multiple of 9. Suppose the person circles the 5 and gives you the three digits sqrambled as 4,6,3. You know the sum of the digits must be a multiple of 9. You add 4+6+3 and get 13. The next multiple of 9 is 18, so you know the circled digit must be 18-13 or 5. Gimme a dollar and I'll tell you how I figured that out. Gimme an extra dollar and I'll tell you how long it took me. Slef E. (The *E* stands for arithmagician) - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 10:02 AM Subject: [RollTideFan] Off season - again... Everyone has to try thisI am now in the phase where I am trying to figure it out http://digicc.com/fido/ DevO __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
RE: [RollTideFan] Off season - again...
You da manMr. Google! -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Jeff Todd Sent: Friday, April 30, 2004 10:35 AM To: RollTideFan-The University of Alabama Athletics Discussion List Subject: Re: [RollTideFan] Off season - again... Not really. I'm just tall enough to look over the smrat kids shoulders when we took tests. :-) And I'm a Google-Eyed Phool! http://tinyurl.com/2y6ok Stick with me, Devo. We'll go places, son! Slef E. - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Friday, April 30, 2004 8:01 AM Subject: RE: [RollTideFan] Off season - again... U R a Gene-E-us! __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
Re: [RollTideFan] Off season - again...
Devo, Every positive integer is a multiple of 9 plus the sum of its digits. Here is why. Take 7843. That's equal to 7×1000 + 8×100 + 4×10 + 3 which equals 7×(999 + 1) + 8×(99 + 1) + 4×(9 + 1) + 3 which equals 7×999 + 7×1 + 8×99 + 8×1 + 4×9 + 4×1 + 3 which equals 7×999 + 7 + 8×99 + 8 + 4×9 + 4 + 3 which equals (7×999 + 8×99 + 4×9) + (7 + 8 + 4 + 3) which equals 9(7×111 + 8×11 + 4) + (7 + 8 + 4 + 3) which equals a multiple of 9 + the sum of the digits. Now when the number is rearranged, that number too is a multiple of 9 plus the sum of its digits. Since the sum of the digits is the same no matter how the digits are rearranged, when you subtract you get a multiple of 9 because the sum of the digits cancel and leave the difference of two multiples of 9, which is a multiple of 9. Since the result must be a multiple of 9, the sum of its digits must also be a multiple of 9. Now you are given all the digits but one, so you add all the digits but one, and that missing digit must be just enough to add to the sum of the other digits to make a multiple of 9. 7843 = multiple of 9 + (7+8+4+3) 4387 = multiple of 9 + (4+7+8+3) --- subtract these 3456 = multiple of 9 - multiple of 9 + (7+8+4+3) - (4+7+8+3) = a multiple of 9 + 0 = a multiple of 9 That multiple of 9 is also a multiple of 9 plus the sum of its digits. Therefore the sum of its digits must also be a multiple of 9. Suppose the person circles the 5 and gives you the three digits sqrambled as 4,6,3. You know the sum of the digits must be a multiple of 9. You add 4+6+3 and get 13. The next multiple of 9 is 18, so you know the circled digit must be 18-13 or 5. Gimme a dollar and I'll tell you how I figured that out. Gimme an extra dollar and I'll tell you how long it took me. Slef E. (The *E* stands for arithmagician) - Original Message - From: Devan Orange [EMAIL PROTECTED] To: 'RollTideFan-The University of Alabama Athletics Discussion List' [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 10:02 AM Subject: [RollTideFan] Off season - again... Everyone has to try thisI am now in the phase where I am trying to figure it out http://digicc.com/fido/ DevO __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
RE: [RollTideFan] Off season
LMBO Krut! -Original Message- krut posted: Have fun! http://fun.from.hell.pl/2003-11-24/bubblewrap.swf __ RollTideFan - The University of Alabama Athletics Discussion List Welcome to RollTideFan! Wear a cup! To join or leave the list or to make changes to your subscription visit http://listinfo.rolltidefan.net
