Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?

Option 4 : The sum of the red and blue lights is equal to the sum of the green and yellow lights

Let the no. of red lights be equal to X and the no. of green lights be equal to Y.

According to the given condition, there exists a blue light for every red light.

Since there are only two lights on each step of the ladder, we can conclude that for every blue light, there exists only one red light. The same condition can be applied to the pair of green and yellow lights.

Thus, we have, no. of red lights = no. of blue lights = X.

Also, no. of green lights = no. of yellow lights = Y.

Therefore, options 1 and 2 are necessarily correct.

Now, the sum of the red and the green lights = X + Y = the sum of the yellow and the blue lights.

Therefore, option 3 is also necessarily correct.

No. of steps of the ladder that have the blue-red pair may be less than the no. of steps that have the green-yellow pair or vice versa.

Hence, option 4 is not necessarily correct.