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Q: Math Teaser ( Answered ,   6 Comments )
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 Subject: Math Teaser Category: Miscellaneous Asked by: djma-ga List Price: \$3.00 Posted: 09 Oct 2003 11:22 PDT Expires: 08 Nov 2003 10:22 PST Question ID: 264649
 `Run this program and tell me why the math works ---- http://digicc.com/fido/`
 Subject: Re: Math Teaser Answered By: bobbie7-ga on 09 Oct 2003 12:09 PDT Rated:
 ```Hello djma-ga, Thank you for Duch an interesting question! Here is how the Fido math puzzle works. “For the sum of numbers less than 9: Subtract 9 from the sum of the numbers given to Fido. That will be your answer.” Example 1) if your numbers are 2331 and you circle 1 then (2+3+3) =8; 9-8 =1 Example 2) 2430 and we circle 2 then (4+3)=7; 9-7=2 Example 3) 4014 and we circle 4 then (4+1)=5; 9-5=4 “If your number is larger than 9 then you need to subtract 9 from it until your subtracted number is less than 9 and then subtract nine again.” Example 1) if your number is 7857 and you circle 5 then 7+8+7 = 22; 22-9 = 13; 13-9 = 4; 9-4=5 Example 2) 3087 and you circle 8 then 7+3=10; 10-9=1; 9-1=8 Example 3) 3762 and you circle 2 then 3+7+6=16; 16-9=7; 9-7=2 Solution courtesy of Stewart Hamel Source: Arachibutyrophobia Website http://www.arachibutyrophobia.com/archives/000190.html There is a discussion about the Fido puzzle at this forum where they also explain how and why this puzzle works. http://www.bpohl.info/forum/index.php?showtopic=99 Here is a more detailed explanation; however, I prefer the first solution I gave you, as it is easier to understand. Take the number 2764 = 2*1000 + 7*100 + 6*10 + 4 = 2(999+1) + 7(99+1) + 6(9+1) + 4 = 2*999 + 2 + 7*99 + 7 + 6*9 + 6 + 4 = (2*999 + 7*99 + 6*9) + 2 + 7 + 6 + 4 = 9(2*111 + 7*11 + 6*1) + (2 + 7 + 6 + 4) = (multiple of 9) + (sum of the digits) “So if you divide this by 9 and take the remainder, that remainder will be the same as the remainder when the sum of the digits is divided by 9.” “Since the second number has the same sum of digits as the first, no matter how you scramble them, they will both leave the same remainder when divided by 9.” “Thus when you subtract, you will get a multiple of 9, because the remainders will cancel. So you divide it by 9 to see what remainder is left. The remainder has to be 0,1,2,3,4,5,6,7, or 8. This tells you what digit was missing from the sum of the digits.” So, If it's 0, the missing digit had to be 9. If it's 1, the missing digit had to be 8. If it's 2, the missing digit had to be 7. If it's 3, the missing digit had to be 6. If it's 4, the missing digit had to be 5. If it's 5, the missing digit had to be 4. If it's 6, the missing digit had to be 3. If it's 7, the missing digit had to be 2. If it's 8, the missing digit had to be 1. http://www.mnemo.nu/?action=view_question&id=96 If the sum of the digits you gave Fido is larger than 9: Divide this number by 9, and then subtract the remainder from 9. That’s the missing number. Example: My number: 1218 Mixed up number: 8112 Difference: 8112-1218= 6894 I circle the number 4 and give Fido the number 689 I add up the digits. 6+8+9=23 I divide it by 9. 23/9= 2 remainder 5 Now I subtract the remainder from 9. 9–5=4 4 is the missing number! If the sum of the digits you gave Fido is less than 9: Subtract this number from 9 and that’s the missing number. Example: My number 1205 Mixed up number: 5210 Difference: 5210-1205 = 4005 I circle the number 5 and give Fido the number 400 I add up the digits 4+0+0=4 Now I subtract this number from 9. 9–4=5 5 is the missing number! Search Criteria: Fido puzzle solution Fido puzzle works I hope this answers your question! Best Regards, Bobbie7-ga```
 djma-ga rated this answer: and gave an additional tip of: \$1.00 `It was answered clearly, concisely and with backup...very well done.`

 Subject: Re: Math Teaser From: bobbie7-ga on 09 Oct 2003 12:40 PDT
 ```Thank you for the nice rating and tip! It was a fun question to answer. --Bobbie7```
 Subject: Re: Math Teaser From: bobbie7-ga on 09 Oct 2003 12:46 PDT
 ```Sorry about the typo: The word "Duch" should be "such"```
 Subject: Re: Math Teaser From: nickdanger-ga on 10 Oct 2003 12:24 PDT
 ```Also, see this page: http://www.wizardofodds.com/askthewizard/askthewizard89.html```
 Subject: Re: Math Teaser From: djma-ga on 10 Oct 2003 12:37 PDT
 `This niceley explains the re-arranging of the numbers point. Neat.`
 Subject: Re: Math Teaser From: g_prime-ga on 13 Oct 2003 19:47 PDT
 ```well i just tried this site thing like 6 or 7 times and it only got the answer right 2 times.. perhaps it doesn't work?```
 Subject: Re: Math Teaser From: djma-ga on 14 Oct 2003 05:56 PDT
 ```I'm pretty convinced it has to work...post your details on an example that doesn't work and let's see if we can see why. My guess is that we will find something.```