Creatively sneaking square roots into HECTOC

Continuing the discussion from Hectoc Strategies:

Say you got a HECTOC starting with:

552___ for 5x5x2 = 50
522___ for 52-2 = 50
455___ for 45+5 = 50

…or another sequence of 3 digits that easily gets you to 50. Next you’d want to get a 2 on the right hand side for a nice 50x2 = 100; however, the next digit is a 4 and you don’t have a square root available (only +, -, x, ÷, ^, and parenthesis)… or do you?

___412 for 4^(1/2) = 2
___424 for 4^(2/4) = 2
___436 for 4^(3/6) = 2
___448 for 4^(4/8) = 2

You can simply use the exponential form of the square root by using the reciprocal of 2 as your exponent. Similarly you can use a cube root by using 1/3 (i.e., the reciprocal of 3):

___813 for 8^(1/3) = 2
___826 for 8^(2/6) = 2
___839 for 8^(3/9) = 2

For those not familiar with the exponential form, this will continue 1/4, 1/5, etc.

826416 for (8+2)^(64^(1/6)) = 10^2

2^6 = 64 so the sixth root of 64 is 2 again

Alternatively, you could of course use 82+6x4x1-6 like any normal person would; but it’s certainly nice to have the additional option of square roots, cube roots, etc. available even though “officially” you don’t… they’re just hidden in plain sight. :wink:

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