There is a string of colored lights hanging in front of the store, which are arranged in a circle according to the order of purple, red, blue and yellow. What colors are the lights No.54, No.69, 109 and 128 respectively? The 54th, 69th, 109 and 128 lights are red, purple, purple and yellow respectively.

According to the meaning of the question, there is a string of colored lights hanging at the door of the shop, arranged in a circular order of purple, red, blue and yellow.

That is, the colored light circulates with a period of 4 bits,

By division, we can get the formula:

54/4= 132

That is, No.54 is the second colored light after the end of 13 cycle, corresponding to red.

And so on:

69/4= 17 1

Therefore, Lantern 69 is purple.

109/4=27 1

So the number 109 is purple.

128/4=32

So the number 128 is yellow.

So the 54th, 69th, 109 and 128 lights are red, purple, purple and yellow respectively.

Extended data:

This kind of problem is the application of remainder property in mathematics.

The remainder has the following important properties (A, B and C are all natural numbers):?

(1) The absolute value of the difference between the remainder and the divisor is less than the absolute value of the divisor (applicable to the real number field);

(2) Dividend = divisor × quotient+remainder;

Divider = (dividend-remainder) ÷ quotient;

Quotient = (dividend-remainder) divider;

Remainder = dividend-divisor × quotient.

(3) If the remainders of A and B divided by C are the same, then the difference between A and B can be divisible by C. For example, if the remainders of 17 and1divided by 3 are 2, then17-1can be divisible by 3.

(4) The sum of A and B divided by the remainder of C (except that A and B divided by C have no remainder) is respectively equal to the sum of the remainder of A and B divided by C (or the remainder of this sum divided by C).

For example, 23, the remainder of 16 divided by 5 is 3 and 1 respectively, so the remainder of (23+ 16) divided by 5 is equal to 3+ 1=4. Note: When the sum of the remainder is greater than the divisor, the remainder is equal to the sum of the remainder and divided by the remainder of C. ..

(5) The product of A and B divided by C is equal to the product of A and B divided by C (or the product divided by C).

For example, 23, the remainder of 16 divided by 5 is 3 and 1 respectively, so the remainder of (23× 16) divided by 5 is equal to 3× 1=3. Note: when the product of the remainder is greater than the divisor, the remainder is equal to the product of the remainder divided by the remainder of C.