For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
11/22/2010

PROBLEM # 1
How many outlines of triangles of all sizes and shapes can you trace in Figure 1?

PROBLEM #2
In a 52 card deck, how many 5-card hands have a single pair and no 3-of-a-kind or 4-of-a-kind?

----------------------------------------------------------------------------------------------------------

Please send your solutions to mr.asaigal@gmail.com.

Use Problem Solutions M-112510 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

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.

-------------------------------------------------------------------------------------------------------------

Problems from 11/11/10

PROBLEM # 1

Four men want to cross a bridge. The bridge is of a width such that a maximum of 2 people may cross at a time. One man takes 10 minutes to cross, another takes 5 minutes to cross, another takes 2 minutes to cross, and the last takes 1 minute to cross. Let's call these men A, B, C, and D, respectively. Here is the catch. If two people cross the bridge together, they must walk at the pace of the slower one. So if A and B cross, they take 10 minutes. Also, it is night. Each trip requires a flashlight. There is only one flashlight. The men are not allowed to toss the light over the river. How fast can you get all 4 men over the bridge?

SOLUTION
19 mins.

PROBLEM #2

John has a miniature Pyramid of Egypt. It is 4 inches in height. John was invited to display it at an exhibition. John felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 3) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid?

SOLUTION
4 cuberoot(3).

Congratulations to Akshay Gowrishankar, Arul Prakash and RK Sambangi, who were winners of the last set of puzzles.

You may also access this article through our web-site http://www.lokvani.com/

Figure 1