Brain Teasers
144 Books
Peter had 144 books and donated them to four schools. When Peter checked the number of books given to each school, he found out that the difference of the number of books between School A and School B was 4; between School B and School C was 3; between School C and School D was 2. School A had the most number of books, but received less than 40 books. How many books did School D get?
Answer
Denote the number of books received by the four schools a, b, c and d, respectively.Since a is the largest, b must equal a-4.
c differs 3 from b, and can be either a-1 or a-7.
If c=a-1, then d must be a-3, which implies a+(a-4)+(a-1)+(a-3)=144, a=38, and a-3=35.
If c=a-7, then d can be either a-5 or a-9. However, it can be checked that in either case, a>=40.
Therefore, School D got 35 books.
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Comments
That one took some notepad scribbling, but I finally got it. I guess I actually DID need those high school math classes!
Whoah! Its hard!
Very nice
It was easier than the solution suggests. With just a little thought it's easily seen that the minimum value for A is with:
A = B + 4
B = C - 3
C = D + 2
Replacing with D gives
D + (D + 2) + (D + 2 - 3) + (D + 2 - 3 + 4) = 144
4D + 4 = 144
4D = 140
D = 35
You really don't need to go through all the other logic.
A = B + 4
B = C - 3
C = D + 2
Replacing with D gives
D + (D + 2) + (D + 2 - 3) + (D + 2 - 3 + 4) = 144
4D + 4 = 144
4D = 140
D = 35
You really don't need to go through all the other logic.
D could be 34 as well. A = 39, B =35, C = 32, D = 34. Sums to 140. Or am i missing something?
Oh duh -- total has to be 144! I wrote 140. My bad.
A= 41
B= 37
C= 34
D= 32
_____
144
D 32 Books
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