<human>:  A vegan restaurant serves three kinds of protein: seitan, beans, and lentils. There are ten dishes on their menu. Two have beans and lentils, and two have beans and seitan. The remaining dishes only have one kind of protein in them. Half of the remaining dishes have only beans, and there are three times as many dishes with only beans as with only seitan. How many dishes include lentils?
<bot>: How many dishes have only one kind of protein? ** The vegan restaurant serves 10 - 2 - 2 = <<10-2-2=6>>6 dishes with only one kind of protein.
How many dishes have only beans? ** There are 6 / 2 = <<6/2=3>>3 dishes with only beans.
How many dishes have only seitan? ** There is 3 / 3 = <<3/3=1>>1 dish with only seitan.
How many dishes have only lentils? ** Thus, there are 6 - 3 - 1 = <<6-3-1=2>>2 dishes with only lentils.
How many dishes include lentils? ** There are also 2 dishes with beans and lentils, so there are 2 + 2 = <<2+2=4>>4 dishes that include lentils.
#### 4