For The Mathematically Inclined


Submitted by Aadhaarshila (ATFS)  The Math and Science Institute 10/06/2003
FOR CHILDREN
PROBLEM # 1
Marty has exactly 5 blue pens, 6 black pens and 4 red pens in his knapsack. If he pulls out one pen at random, what is probability that the pen is either red or black? PROBLEM # 2
The average of 20, 70 and x is 40. If the average of 20, 70 , x and y is 50, then y is = ?
FOR GROWN UPS
PROBLEM # 3
You own a factory that makes metal patio sets using two processes. The hours of
unskilled labor, machine time and skilled labor per patio set are given in the table below.
You can use up to 4000 hours of unskilled labor, up to 1500 hours of machine time and
up to 2300 hours of skilled labor. How many patio sets should you make by each process to
maximize profits, which is $80 for a patio made by Process A and $40 for a patio made by
Process B?
Assembly Hours  Process A  Process B 
Unskilled labor  10  1 
Machine Time  1  3 
Skilled Labor  5  2 

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 SOLUTIONS TO PROBLEMS ON 9/11/03
PROBLEM # 1
Determine the ones digit for the expression:
0! + 1! + 2! + 3! + 4! + . . . + 9999! + 10000!
SOLUTION
0! = 1 and the ones digit for 5! and above = 0.
Therefore, the ones digit for the expression is 4. PROBLEM # 2
What three consecutive counting numbers have a sum which is 0.2 of their product?
SOLUTION
There are three solutions:
5, 4, 3
1, 0, 1
3, 4, 5
Winners
Congratulations to P. Jain, L. Padmanabhan, A. Sangoram, A. Shah and B. Venkataraman, who were all winners of the last puzzle.

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