# Question:How to solve this system with floors?

## Question:How to solve this system with floors?

Maple 2018

I mean, for example,

```solve({4*x1+7*x2+6*x3 = 186, floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18,
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21});
Warning, solutions may have been lost

```

A finite number of the solutions can be found by DirectSearch

```DirectSearch:-SolveEquations([floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18,
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21, 4*x1+7*x2+6*x3 = 186],
{x1 >= -100, x2 >= -100, x3 >= -100, x1 <= 100, x2 <= 100, x3 <= 100},
AllSolutions, solutions = 3, number = 1000);

Matrix(3, 4, [[0., Vector[column](3, [0., 0., 0.]),
[x1 = 74.18778903830886, x2 = 58.93905207777524, x3 = -87.22075344961036], 185],
[0., Vector[column](3, [0., 0., 0.]),
[x1 = 71.22714241634635, x2 = 56.43467122661542, x3 = -82.32521137528222], 164],
[0., Vector[column](3, [0., 0., 0.]),
[x1 = 73.6407870507502, x2 = 58.33738250527096, x3 = -86.15413762331626], 165]])```

I don't see a way to obtain the MMA answer (in Maple notation)

```(155/2 < x1 and x1 < 78 and 744/7-4*x1*(1/7) < x2 and x2 < 62 or 72 <= x1 and x1 <= 73 and
102-4*x1*(1/7) < x2 and x2 < 62 or 73 < x1 and x1 <= 147/2 and 102-4*x1*(1/7) < x2 and
x2 <= 726/7-4*x1*(1/7) or 147/2 < x1 and x1 < 74 and 60 <= x2 and x2 <= 726/7-4*x1*(1/7) or
74 <= x1 and x1 < 75 and 726/7-4*x1*(1/7) < x2 and x2 < 62 or 153/2 < x1 and x1 < 78 and
726/7-4*x1*(1/7) < x2 and x2 < 60 or x1 = 72 and 58 <= x2 and x2 < 60 or 72 < x1 and x1 < 74 and
58 <= x2 and x2 <= 708/7-4*x1*(1/7) or 75 <= x1 and x1 < 76 and 102-4*x1*(1/7) < x2 and x2 < 60 or
x1 = 74 and 442/7 < x2 and x2 < 64 or 74 < x1 and x1 < 75 and 738/7-4*x1*(1/7) < x2 and
x2 <= 744/7-4*x1*(1/7) or 74 <= x1 and x1 < 75 and 708/7-4*x1*(1/7) < x2 and x2 <= 102-4*x1*(1/7) or
151/2 < x1 and x1 < 76 and 708/7-4*x1*(1/7) < x2 and x2 < 58 or 157/2 < x1 and x1 < 80 and
762/7-4*x1*(1/7) < x2 and x2 < 64 or 68 <= x1 and x1 < 137/2 and 56 <= x2 and x2 <= 666/7-4*x1*(1/7) or
x1 = 137/2 and x2 = 56 or x1 = 70 and 56 < x2 and x2 < 58 or 70 < x1 and x1 <= 71 and 56 <= x2 and
x2 < 58 or 71 < x1 and x1 < 72 and 56 <= x2 and x2 <= 690/7-4*x1*(1/7) or 70 <= x1 and x1 <= 281/4 and
54 <= x2 and x2 < 55 or 281/4 < x1 and x1 < 72 and 54 <= x2 and x2 <= 666/7-4*x1*(1/7)) and
x3 = 31-2*x1*(1/3)-7*x2*(1/6)```
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