For The Mathematically Inclined

Problem 1
How many times do the two hands of a clock point in the same direction between 6:00 am and 6:00 pm of a single day?

Problem 2
I woke up one night and heard my clock strike "one." I was too tired to turn on the light to see what time it was. As I lay there pondering, it occurred to me to speculate how long I would have to lie awake in order to be sure what was the exact time. My clock strikes the hours and strikes "one" each half hour. I fell asleep before I solved the problem, but can you work out what is the longest time I would have to lie awake after hearing the strike "one," to be sure of the time?

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

Please send your solutions anil@lokvani.com.

Use Problem Solutions M-022516 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.

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

Problem 1

Can you find four consecutive prime numbers that add up to 220 ?

Problem 2

Find three positive whole numbers that result in same number when added together or multiplied together.

Congratulations to Avanish Gowrishankar, Meena Kaushik and Amit Lele, who were the winners of last set of puzzles.