SOLUTION: Six students each try to guess the number of pennies in a jar. The six guesses are 52, 59, 62, 65, 49, and 42. One guess is 12 away, and the other guesses are 1, 4, 6, 9, and 11 aw

Question 152341: Six students each try to guess the number of pennies in a jar. The six guesses are 52, 59, 62, 65, 49, and 42. One guess is 12 away, and the other guesses are 1, 4, 6, 9, and 11 away. How many pennies are in the jar?
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
This is a problem of statistics. Instead of get bogged down in statistics language and symbols, let's take a straightforward approach:
First, let's make a few observations: The MOST pennies there will be will be 65+12=77. The LEAST pennies there will be will be 42-12=30. So we know that 30 Now,
|x+a|=1
|x+b|=4
|x+c|=6
|x+d|=9
|x+e|=11
|x+f|=12
gives a set of numbers {a,b,c,d,e,f} such that the magnitude of the difference (+ or -) from x is our set of incorrect guesses.
Most interesting here, we can note the last two equations. We have to have two numbers that are either precisely 1 away from each other, or precisely 23 away from each other. We see that this can only happen with 65 and 42 from our number set. 65-11 or 65-12 must be our number. But we need 42+11 or 42+12 to be that same number. So 53 or 54 is our number.
And right away we can notice that if a number is 1 away, that we must be dealing with 53 due to the presence of 52 in our original number list. (54-1=53, not on the list)
So our x is 53.
And to check that we can say:
53-1=52
53-4=49
53+6=59
53+9=62
53-11=42
53+12=65
This all follows.
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