There is a string of red and blue lights strung around a window. the red lights blink every 3 seconds , and the blue lights blink every 5 seconds. how many times will they blink at the same time in one minute? ?

To answer this question, we need to determine how many common multiples there are between 3 and 5, that are lower than 60.

It turns out that every common multiples of 3 and 5 is also a multiple of 15. So, there are (60/15) = 4 such common multiples.
So the answer is 4.

Here is a more detailed description:

After 1 seconds:
The red lights don't blink
The blue lights don't blink

After 2 seconds:
The red lights don't blink
The blue lights don't blink

After 3 seconds:
The red lights blink
The blue lights don't blink

After 4 seconds:
The red lights don't blink
The blue lights don't blink

After 5 seconds:
The red lights don't blink
The blue lights blink

After 6 seconds:
The red lights blink
The blue lights don't blink

After 7 seconds:
The red lights don't blink
The blue lights don't blink

After 8 seconds:
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The blue lights don't blink

After 9 seconds:
The red lights blink
The blue lights don't blink

After 10 seconds:
The red lights don't blink
The blue lights blink

After 11 seconds:
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After 12 seconds:
The red lights blink
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After 13 seconds:
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After 14 seconds:
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After 15 seconds:
The red lights blink
The blue lights blink
They have blinked at the same time 1 times

After 16 seconds:
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The blue lights don't blink

After 17 seconds:
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After 18 seconds:
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After 19 seconds:
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After 20 seconds:
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After 21 seconds:
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After 24 seconds:
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After 27 seconds:
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After 28 seconds:
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After 29 seconds:
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After 30 seconds:
The red lights blink
The blue lights blink
They have blinked at the same time 2 times

After 31 seconds:
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After 32 seconds:
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After 33 seconds:
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After 36 seconds:
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After 38 seconds:
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After 39 seconds:
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After 40 seconds:
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After 41 seconds:
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After 42 seconds:
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After 43 seconds:
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After 44 seconds:
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After 45 seconds:
The red lights blink
The blue lights blink
They have blinked at the same time 3 times

After 46 seconds:
The red lights don't blink
The blue lights don't blink

After 47 seconds:
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After 48 seconds:
The red lights blink
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After 49 seconds:
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After 50 seconds:
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After 51 seconds:
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After 52 seconds:
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After 53 seconds:
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After 54 seconds:
The red lights blink
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After 55 seconds:
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The blue lights blink

After 56 seconds:
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After 57 seconds:
The red lights blink
The blue lights don't blink

After 58 seconds:
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After 59 seconds:
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After 60 seconds:
The red lights blink
The blue lights blink
They have blinked at the same time 4 times

There is no association.