Solve the system:
x + ⌊y⌋ + {z} = 3.141
⌊x⌋ + {y} + z = 2.718
{x} + y + ⌊z⌋ = 1.618
Where ⌊p⌋ is the floor function and {p} is the fractional part function.
Consider the lhs of the three equations as a 3x3 array.
Then, the sum of the first column =x+[x]+{x} =2x
Similarly, the sum of the second and third columns are respectively 2y and 2z.
Therefore, adding the three given equations, we must have:
2(x+y+z) = 7.477
=> x+y+z= 3.7385 .....(I)
Subtracting each of the three given equations from (I), we obtain:
-> {y}+[z]= 0.5975, so that: [z]=0, and {y}= 0.5975
-> {x} + [y] =1.0205, so that: [y] =1, and {x} = 0.0205
-> [x]+{z}= 2.1205, so that: [x]=2, and {z}=0.1205
Consequently, we must have:
x= [x]+{x} = 2.0205
y= [y]+{y} = 1.5975
z= [z] +{z} = 0.1205
Edited on September 18, 2022, 7:20 am
Puzzle Solution
