Question

Lemonade. You want to buy a new car, and you know the model you want. The model has three options, each one of which you can either take or not take, and you have a choice of four colors. For example, you can say yes or no to a spoiler, to leather seats, and to GPS. So far 100,000 cars of this model have been sold. What is the largest number of cars that you can guarantee to have the same color and the same options as each other?

Answer 1

3125

Explanation:

The model has three options, each one of which you can either take or not take.

Let us represent taking an option with 1 and not taking an option with 0

1. 0 0 0 ( taking none of the options)

2. 0 0 1

3. 0 1 0

4. 0 1 1

5. 1 0 0

6. 1 0 1

7. 1 1 0

8. 1 1 1 ( taking all three options)

Also you have a choice of four different colors, therefore, total number of possible combinations are

8*4= 32

Hence the largest number of cars having same options and colors is

100,000/32

3125 cars