Question

professor x is getting ready to teach a class. as usual, he needs to bring three markers for writing on the board: one red, one green, and one blue. his office is dark and he cannot see the colors of the markers. but his supply box has twenty markers: ten red markers, seven green markers, and three blue markers. how many markers would professor x have to grab to make sure that he has one set of red-green-blue markers? explain your reasoning.

Answer 1

To ensure Professor X has a complete set of red, green, and blue markers, he would need to grab a total of 18 markers due to the possibility of selecting all markers of one color first.

Step-by-step explanation:

The student's question asks how many markers would Professor X need to grab to ensure he has a complete set of red, green, and blue markers.

To solve this puzzle, think about the worst-case scenario. If Professor X grabs markers blindly, he could pick all the markers of one color before finding a marker of a different color.

The largest quantity of markers of a single color in the supply box is red (10 markers).

So, if Professor X were unlucky, he could pick all 10 red markers before finding a green or blue one.

Next, he could potentially pick all seven green markers before finding a blue one.

Finally, the next marker he picks must be blue, as that's the only color he hasn't picked yet.

So, in total, Professor X would need to grab 10 (red) + 7 (green) + 1 (blue) = 18 markers to guarantee he has at least one of each color for his class.