Arrange 4 fours into various expressions to generate all integer numbers, from 1 to 112 inclusive like:
1 = 44 ÷ 44
2=sqrt 4 - (4 - 4) x 4
3 = (4 + 4 + 4) ÷ 4
4 = 4 + 4 × (4 - 4)
... ...
7= 44/4-4
... ...
19=4!-4-4/4
... ...
100=4*4!+sqrt(4*4)
etc
Allow use of concatenation, +, -, x, /, sqrt, exponentation, factorial,decimal fractions, overline & brackets.
Source: Inspired by Martin Gardner statement.
Once the 113 would be resolved Charlie’s original list plus the “seven magnificent “ additions would extend the list till 120, thus enabling it to be farther extended:<p>
120=(4+4/4)! <br>
121=(44/4)^(sqrt4) <br>
122= (4+4/4)! +(sqrt4) etc
I might go further, but I prefer to challenge all of you , what will be the current Nn provided 113 is presented by 4 fours
113= (44/4) & sqrt(!4) using concatenation (&) and the subfactorial (!x sign),
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added on Oct 6:<p>
the concatenation between expressions is not a necessity, one may replace it by simple addition:<p>
113=44/.4 + sqrt(!4)<p>
I will definitely publish a sequel to this solution and might use the concatenationn between expressions when there is no other choice.
Edited on October 6, 2023, 10:27 pm
Extending the puzzle
