Wednesday, June 12, 2019

mathematics - 6, the magic number


Here's a fun (albeit difficult) one:


Make these equations true using arithmetic operations:


1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6

8 8 8 = 6
9 9 9 = 6

For example: 6 + 6 - 6 = 6 (I hope I did not spoil some of you :D)


Allowed operators are:


+, -, *, /, ! , ^, %

Setting parenthesis is also allowed.


The ^ operator is an exception as you are permitted to supply a second argument to it which may be any positive integer or the multiplicative inverse of it.


x1/y is always positive and real.



If you find an alternative solution using other operators you may post it but please also provide a solution using only these 7 operators.




For those of you who think this was easy, here is a bonus:


0 0 0 = 6

Answer



1.



(1+1+1)!=6



2.




2+2+2=6



3.



333=6



4.



(444)!=4+4+4=6




5.



5+55=6



6.



666=6+66=6



7.




777=6



8.



(8+88)!=6



9.



(999)!=6




Bonus:



(0!+0!+0!)!=6



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