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For The Mathematically Inclined

Anil Saigal
06/03/2005

FOR CHILDREN

PROBLEM # 1
In the number 98765.43, the place occupied by the digit nine is how many times greater than the place occupied by the digit 3?

FOR GROWNUPS

PROBLEM # 2
A clock hangs on the wall of a railway station. The dimensions of the wall are 71 feet 9 inches long and 10 feet 4 inches high. While waiting for a train, you notice that the hands of the clock were pointing in opposite directions and were parallel to one of the diagonals of the wall. What was the exact time?

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Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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SOLUTIONS TO PROBLEMS ON 06/02/05

FOR CHILDREN

PROBLEM # 1
You have a large wooden cube that measures 4 feet on each edge. You need to cut the cube into 64 smaller cubes that measure 1 foot on each side. If you rearrange the pieces before each cut, what is the least number of cuts you will have to make?

SOLUTION
9.

FOR GROWNUPS

PROBLEM # 2
Each shaded triangle in the circle is equilateral with side lengths of one unit. Find the length of the radius of the circle. (Figure 1)

SOLUTION
0.5*(Tan60 + Tan54).

Congratulations to Bipin Parekh, Ameek Ponda, Neha Sharma, Ramya Tammisetti, Dharmesh Thakkar and Raj Vishwanathan, who were winners of the last set of puzzles.



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Figure 1

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