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 No Addition Allowed (Posted on 2009-12-14)
Without using addition, make five 6s to equal 30.
Without using addition, make six 7s to equal 42.

The calculations should be exact (no rounding functions). Any common symbols or operators other than addition are allowed.

Replacing addition with subtracting a negative is NOT a solution.

 See The Solution Submitted by Brian Smith Rating: 2.0000 (1 votes)

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 triangular numbers | Comment 5 of 6 |

Both 36 and 42 are  (2* a triangular number) and can be derived from either t=m*m+m or t=n*n-n iff n=m+1.

The second expression uses 3 digits only i.e. 6*6-6 or 7*7-7

To get an extra digit - replace one of the digits by
sqrt of its second power e.g. 6==>sqrt(6*6)

To get an extra  k (k>1) digits - multiply the outcome of the generic 3-digits solution by 6/6 raised to a power  kkkkkkk....k (concatenation of k-2 sixes). If k=2 ,the exponent is zero,
leaving just 6/6.
Of course ,the above method is applicable to 7 and to other digits.

I wonder, why the official solution requires different answers for 6 and 7.

BTW  66-6*6=30   unique for 6

Edited on December 15, 2009, 6:02 am
 Posted by Ady TZIDON on 2009-12-15 05:56:22

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