Each of three players has written a list of 100 words. The lists are compared and all the words that appear in at least two lists are crossed out. Is it possible that 54 words remain in the first list, 75 in the second and 80 in the third?
the 1st list has 46 words crossed out ... 100 - 54
the 2nd list has 25 words crossed out ... 100 - 75
the 3rd list has 20 words crossed out ... 100 - 80
the sum of the 2nd and 3rd lists is 45 ... 25 + 20
this is NOT enough to cancel the 46 words in the 1st list
not possible
To determine whether it is possible for 54 words to remain in the first list, 75 words in the second list, and 80 words in the third list, we need to analyze the numbers.
Since there are 100 words on each list, let's start by finding the maximum number of words that could be crossed out to ensure that the remaining numbers are possible.
In order for there to be 54 words remaining in the first list, there could have been at most (100 - 54) = 46 words crossed out.
For 75 words remaining in the second list, there could have been at most (100 - 75) = 25 words crossed out.
Similarly, for 80 words remaining in the third list, there could have been at most (100 - 80) = 20 words crossed out.
Now, let's check if these numbers are compatible.
If all the words that are crossed out from the first list are from the second and third lists, then a maximum of 46 words could be crossed out from the first list. However, the second list only allows for a maximum of 25 words to be crossed out. Since 46 > 25, it is not possible for 54 words to remain in the first list.
Hence, it is not possible for 54 words to remain in the first list, 75 words in the second list, and 80 words in the third list.