bonanova Posted July 11, 2009 Report Share Posted July 11, 2009 An old favorite asks us to express the integers using only four 4's. For example: 1 = 44/44; 2 = 4/4 + 4/4. Irrationally perhaps, it has been suggested that we use pi instead. We are allowed the operations of addition, subtraction, multiplication, division, square root and floor. Floor, indicated by brackets, is simply the largest whole number: 3 = [pi]. Can you express the numbers 1-20 using 4 or fewer pi's? Using spoilers, of course. Enjoy. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 11, 2009 Report Share Posted July 11, 2009 Reveal hidden contents 0 = pi - pi 1 = [sqrt(pi)] 2 = [pi] - pi/pi 3 = [pi] 4 = [pi] + pi/pi 5 = [pi] + [pi] - pi/pi 6 = [pi] + [pi] 7 = [pi] + [pi] + pi/pi 8 = [pi]*[pi] - pi/pi 9 = [pi]*[pi] 10 = [pi]*[pi] + pi/pi 11 = [pi]*[pi] + [pi] - [sqrt(pi)] 12 = [pi]*[pi] + [pi] 13 = [pi*pi + pi] 14 = [pi*pi + pi] + [sqrt(pi)] 15 = [sqrt(pi)*pi*pi - sqrt(pi)] 16 = [[pi]*([pi]+[pi]) - sqrt(pi)] 17 = [[pi] * (pi+pi)] - [sqrt(pi)] 18 = [[pi] * (pi+pi)] 19 = [pi * ([pi]+pi)] 20 = [pi * (pi+pi)] Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 11, 2009 Report Share Posted July 11, 2009 (edited) On 7/11/2009 at 9:44 AM, bonanova said: An old favorite asks us to express the integers using only four 4's. For example: 1 = 44/44; 2 = 4/4 + 4/4. Irrationally perhaps, it has been suggested that we use pi instead. We are allowed the operations of addition, subtraction, multiplication, division, square root and floor. Floor, indicated by brackets, is simply the largest whole number: 3 = [pi]. Can you express the numbers 1-20 using 4 or fewer pi's? Using spoilers, of course. Enjoy. No parentheses? Reveal hidden contents Assuming order of operations holds, and only addition, subtraction, multiplication, division, sqaure root and floor (no parentheses) allowable: 1 = pi/pi 2 = pi/pi + pi/pi 3 = [pi] 4 = [pi] + pi/pi 5 = [pi] + [pi] - pi/pi 6 = [pi] + [pi] 7 = [pi] + [pi] + pi/pi 8 = [pi] * [pi] - pi/pi 9 = [pi] * [pi] 10= [pi] * [pi] + pi/pi 11= [pi] * [pi] + [pi] - [sqrt(pi)] 12= [pi] * [pi] + [pi] 13= [pi] * [pi] + [pi] + [sqrt(pi)] 14= [sqrt(pi) * pi * pi - pi] 15= [pi] * [pi] + [pi] + [pi] 16= [pi * pi + pi + pi] 17= [sqrt(pi * pi * pi) * pi] 18= [pi] * [pi] + [pi * pi] 19= pi * pi + pi * pi 20= [sqrt(pi) * pi * pi + pi] Edited July 11, 2009 by tomaketu Quote Link to comment Share on other sites More sharing options...
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bonanova
An old favorite asks us to express the integers using only four 4's.
For example: 1 = 44/44; 2 = 4/4 + 4/4.
Irrationally perhaps, it has been suggested that we use pi instead.
We are allowed the operations of addition, subtraction, multiplication, division, square root and floor.
Floor, indicated by brackets, is simply the largest whole number: 3 = [pi].
Can you express the numbers 1-20 using 4 or fewer pi's?
Using spoilers, of course.
Enjoy.
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