Friday, October 4, 2019

mathematics - Something is wrong with the equation



There is something wrong with the equation below:


enter image description here



By just exchanging two squares at a time, find the equality with the least amount of exchange.



For example if this question is asked for below equation, you may find the solution with one time exchange:


enter image description here


the answer will be exchanging "+" and "9" which makes the equation correct as below:



29+5=34




FYI: Even though it is not a hint, all numbers are used only once. (0,1,2,3,4,5,6,7,8,9)


Hint: you only swap each square once for optimal clear solution.



Answer



@oray's edit: Here is my intented answer since no-one found it out:



3140×(6+9)=275×8 (Initial layout)
3140×(6+9)2=75×8 ("=" and "")
3×40×(6+9)2=7518 ("×" and "1")
3×45×(6+9)2=7018 ("0" and "5")

3×45×(6+9)7=2018 ("2" and "7")



which is



the year we are in.



I found another solution with



4 exchanges




which is:



3140×(6+9)=275×8 (Initial layout)
3+40×(619)=275×8 (Swapped 1 and +)
3+40=(619)×275×8 (Swapped = and ×)
3+40=(629)×175×8 (Swapped 2 and 1)
5+40=(629)×173×8 (Swapped 5 and 3)
To arrive at 45=45



————————————————————————————————————————————



Original post: I'm not sure if this is optimal, but I can do it in



4 exchanges



like this:



3140×(6+9)=275×8 (Initial layout)
314×0(6+9)=275×8 (Swapped 0 and ×)
314×0(6+9)=275×8 (Swapped 7 and )
314×0(6+8)=275×9 (Swapped 8 and 9)

514×0(6+8)=273×9 (Swapped 3 and 5)
To arrive at 0=0.



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