Think of a number with two digits. For example, 43. Follow the Magic Gopher's instructions and he will amaze you by telling you what number you chose.

Language level:

### Discussion

Did he get your number right? How does he do it?!

98x
2x
AliciaRockman 8 December, 2013 - 04:25

I know the trick! If you subtract the sum of any 2-digit number from itself, it always results in any of 9's one or two-digit multiples... and if you check the sheet, all of 9's multiples are having the same symbol! So easy!

0 users have voted.
273x
3x
Larry 1 December, 2013 - 04:39

UHH
It is changing the symbol and if i didn't think 43 then it's magic is finish. The symbol it shows is always 36 symbol..

0 users have voted.
4371x
27x
princessred124 10 November, 2013 - 16:51

Everytime it changes the symbol of multiple of 9. Whenever we plus the two digits numbers and minus with the original numbers the answer which comes is always multiple of 9. He knows what is the multiple of 9 and shows the symbol to you........Simple and easy!!!! Watch carefully and you'll understand it

0 users have voted.
229x
4x
Apocalypse 6 November, 2013 - 10:36

I got it. All your answers can be divided by 9. He uses one symbol for all of these numbers and shows it to you.

0 users have voted.
105892x
781x
Jonathan - Coor... 11 October, 2013 - 05:25

Hi avhie18! Have you worked out what the trick is? :)
Jonathan (LearnEnglish Teens Team)

0 users have voted.
105892x
781x
Jonathan - Coor... 3 October, 2013 - 02:25

Hi Yassine! Good guess but let me assure you that Magic Gopher doesn't use the camera. Can you think of another explanation ... ? I hope you enjoy solving this puzzle.
Jonathan (LearnEnglish Teens Team)

0 users have voted.
354x
3x
FAFMIR 18 September, 2013 - 18:40

The trick to the game is that the gopher uses the same symbol for every multiple of 9, from 0 through 81 (it is impossible to get a higher number using only two digits). The gopher assigns the same symbol to the multiples of 9 as to other non-multiples of 9 in order to cover up the trick; the symbol picked for each game is randomized. No matter which two-digit integer the player chooses, when the subtraction is done, the resulting number will always be a multiple of 9. In fact, no matter which (nonnegative) integer the player chooses, the result will always be a multiple of 9. The former can be proven using elementary algebra. Be aware that the proofs for n digits rely on that the digits of the number n\, are indexed with the rightmost digit being assigned position 0, with the adjacent digits (to the left) having an index increasing by one each time. For example, for the number '261', the digit '1' is in position 0, '6' is in position 1, and '2' is in position 2.

0 users have voted.