Tchisla is claiming new better target 1 solutions? #8
Description
Tchisla (on IOS) is claiming there's an improvement to the following puzzles, that these are no longer the optimum solutions:
2 / 2 = (2 - 2)! = 1
3 / 3 = (3 - 3)! = 1
4 / 4 = (4 - 4)! = 1
9 / 9 = (9 - 9)! = 1
This gives us 1 number, and any number of SQRT and factorial.
Real numbers exist, but not complex numbers. Neither operation works with negative numbers, and factorial only works with non-negative integers (including 0, and 0! = 1). There's an upper limit on number magnitude.
Following these rules, 1 is the only real value that can be operated on with square root to reach 1. Non-integer values between 0 and 2 can never be mutated with SQRT to a value that can be acted upon by factorial either.
Lets try:
SQRT(2) = 1.4…
2! = 2
SQRT(3) = 1.7…
3! = 6
SQRT(3!) = 2.4…
SQRT(SQRT(3!)) = 1.5…
3!! = 720
SQRT(3!!) = 26.8…
SQRT(SQRT(3!!)) = 5.1…
SQRT(SQRT(SQRT(3!!))) = 2.2…
SQRT(SQRT(SQRT(SQRT(3!!)))) = 1.5…
3!!! = too big
SQRT(4) = SQRT(4)! = 2
SQRT(SQRT(4)) = 1.4…
4! = 24
SQRT(4!) = 4.8…
SQRT(SQRT(4!)) = 2.2…
SQRT(SQRT(SQRT(4))) = 1.4…
4!! = 62…00
SQRT(4!!) = 78…22+76/81
SQRT(SQRT(4!!)) = 887516.4…
SQRT(SQRT(SQRT(4!!))) = 942.08…
SQRT(SQRT(SQRT(SQRT(4!!)))) = 30.6…
SQRT(SQRT(SQRT(SQRT(SQRT(4!!))))) = 5.5…
ST(ST(ST(ST(ST(ST(4!!)))))) = 2.3…
ST(ST(ST(ST(ST(ST(ST(4!!))))))) = 1.5…
4!!! = to big
SQRT(9) = 3
SQRT(SQRT(9)) = 1.7…
SQRT(9)! = 6
SQRT(SQRT(9)!) = 2.4…
SQRT(SQRT(SQRT(9)!)) = 1.5…
SQRT(9)!! = 720
SQRT(SQRT(9)!!) = 26.8…
SQRT(SQRT(SQRT(9)!!)) = 5.1…
SQRT(SQRT(SQRT(SQRT(9)!!))) = 2.2…
SQRT(SQRT(SQRT(SQRT(SQRT(9)!!)))) = 1.5…
SQRT(9)!!! = too big
9! = 362880
SQRT(9!) = 602.3…
SQRT(SQRT(9!)) = 24.5…
SQRT(SQRT(SQRT(9!))) = 4.9…
SQRT(SQRT(SQRT(SQRT(9!)))) = 2.2…
SQRT(SQRT(SQRT(SQRT(SQRT(9!))))) = 1.4…
9!! = too big
That was overkill, but it does explore all the options, reaching dead ends.
So either it's a bug on my end, or a bug in the online (I assume) database, or I've missed something important in the gameplay, or it's something like the following causing a bug:
3 - 2 = 3 - - - 2 = 1
3 - - 2 = 3 - - - - 2 = 5
3 * + 2 = 3 * + + 2 = 5