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 |