Magic Gopher Explained
What is the Magic Gopher?
Click here to find out.
I have been asked to explain this.
If you look at the chart at the end of the trick, it is no coincidence that the numbers 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90 all have the same symbol. This is because no matter what two digit number you pick, you always end up with one of those numbers after all of the calculations are done.
Lets say you pick a number in the 30's. It doesn't matter what number you pick, they all end up, once you do the math, being 27.
31-(3+1)=27
32-(3+2)=27
33-(3+3)=27
34-(3+4)=27
No matter what number you pick to be in the "ones" digit, you end up subtracting that same digit from the original number, and you're left with a multiple of 10 (in this case 30.) As the number you pick gets higher, the number you subtract gets higher.
Therefore, your number will always be one of 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, or 90, and because all of those numbers have the same sign, the gopher is able to correctly guess the sign every time.
Click here to find out.
I have been asked to explain this.
If you look at the chart at the end of the trick, it is no coincidence that the numbers 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90 all have the same symbol. This is because no matter what two digit number you pick, you always end up with one of those numbers after all of the calculations are done.
Lets say you pick a number in the 30's. It doesn't matter what number you pick, they all end up, once you do the math, being 27.
31-(3+1)=27
32-(3+2)=27
33-(3+3)=27
34-(3+4)=27
No matter what number you pick to be in the "ones" digit, you end up subtracting that same digit from the original number, and you're left with a multiple of 10 (in this case 30.) As the number you pick gets higher, the number you subtract gets higher.
Therefore, your number will always be one of 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, or 90, and because all of those numbers have the same sign, the gopher is able to correctly guess the sign every time.
Comedy
113 comments:
How in the world did you figure this out? Was it simply by doing a bunch of different numbers and then realizing what what happening?
No. I sort of just saw it as I was doing the original calculations.
Jeff
You did an excellent job figuring this out and explaining it clearly. Good work.
Seems to me though that you had to do more than just see the solution as you were doing the natg,
Grandpa
Here's an alternate explanation:
Let's say you pick the 2-digit number ab. ab = a*10 + b.
Adding the two digits together is just a + b. Subtracting that gives:
a*10 + b - (a + b) = 9a. Like Jeff pointed out, b doesn't matter, and no matter what a is, 9a is a multiple of 9 (all multiples of 9 were given the same symbol).
Its kinda sad that it took you this long to figure out how it works... :[
I Just saw this today for the first time and wanted to know how it worked. Problem is I tried it several different times, but the symbol I ended up with was different each time, and the gopher still guessed it. How do you explain that?
The symbols associated with the numbers change each time the game is played. :)
Although I realse that it is impossible that a gopher could read my mind, this is a very clever mathematical conundrum.
These types of 'tricks' are usually exceptionally easy to work out. It did take me several minutes to work out how the gohpher was doing it in this game.
JEFF HAHA U R WRONG! lets see, IF U DONT DO THE MATH AND EVERYTHING, AND HEY GUESS WHAT?! HE DOESN'T PICK THAT EXACT SYMBOL FOR 9, 18, AND SO ON EVERY TIME! HE CHOOSES DIFFERENT ONES TO!
OH! YOU ARE DOWN RIGHT WRONG!
LIKE OMG JEFF! JEEZUS U NEED TO GO BACK TO COLLEGE....OR PRESCHOOL! U ARE SOOOOO WRONG ITS NOT EVEN FUNNY! NEXT TIME DONT POST SOMETHING SO UNTRUE AS UR BRAIN WORKING ITS BAD KNOWLEDGE!
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