Anne, Edward, and Isaac are the three editors of the Perplexus Weekly newspaper. This week, Anne spotted 300 errors, Edward spotted 100 errors, and Isaac spotted 200 errors. Altogether, they spotted 404 errors. Assuming that each error is equally easy to spot, about how many errors did they miss?

The answer is not 196 (thanks Charlie).

The answer IS 96.  The total number of errors is 500.

Anne caught 60%, Edward:40%, and Isaac 20%.

Anne caught 300 which included 120 that Edward saw and 60 that Isaac saw.  Now Anne, Edward and Isaac had a common pool of 500*0.6*0.4*0.2 = 24.

Edward and Isaac spotted 40 together.

Summing: Anne saw 300.

Edward saw 200 minus the 120 already seen by Anne = 80

Isaac saw 100 minus the 60 already seen by Anne and the 40 seen by Edward. This would total 0, however the 60 and the 40 both include the 24 seen by all. So . . . Isaac saw 24 alone.

This totals 404 errors.

Now what is wrong with my logic?

Edited to correct simple, but grevious, subtraction error.

Edited on February 14, 2006, 2:50 pm

Posted by Leming on 2006-02-14 14:41:24