The Whole Problem

E4
A word about tough problems. I hear you both ways: either you say the puzzles are so easy that you need to be in junior high to solve them or you say nothing if they're way beyond your solving powers. So what's a puzzle setter to do? Well, here's what - I run them again after your stunning silences. And that goes for the second problem in the endgame section. Let's see if anyone can get it now.
Meanwhile. A starts digging a hole at 'a' inches per minute. After 12 minutes, B starts digging his own hole at - what else? - 'b' inches per minute (b < a). B's hole being very close to A's hole, the dirt from his hole falls into A's hole. A yells blue murder but B cannot hear him. So poor A has to shovel out B's stuff as he keeps digging. Now 'x' minutes later, the depth of A's hole is equal to his height and also the depth of B's hole equals his height. If A and B are both shorter than seven feet, if six times A's height equals seven times B's height and if everything is integral, how long did A dig? 
DEAR MS
(The problem concerned each of the letter pairs OM, YN, ON, IV, OL, UB, EC except one, that fit inside a 5-letter word. The same three letters, in order, complete each 5-letter word. - MS) 
See-I-See Dept:
The answer is CIC, which yields COMIC, CYNIC, CIVIC, COLIC AND CUBIC. CECIC does not fit, as per the question.
- Murali Krishnamurthy, murali_km@hotmail.com
 
The three letters are CIC: COMIC, CYNIC, CONIC, CIVIC, COLIC, CUBIC. I don't think CECIC is a word.
- Adriano,?write2lance@gmail.com
(The other problem was: "How many runs can a single player (batsman) score in a One Day Match of 50 overs or 300 balls duration? There are no 'no balls', no wides, no overthrows, no extras of any sort. - MS)
 
Over-In-A-Run Dept:
The answer is 1,653 runs. In the first 49 overs of the match, the batsman scores 5 sixes in the first 5 balls and takes 3 runs off the last ball so that he faces the next over. In the last over, the batsman hits 6 sixes. In total, he scores (5*6*49) + (1*3*49) + (6*6*1) = 1,653 runs.
- Manoj Joshi, ?mjoshi8@yahoo.com
 
The answer is 1,653. He opens the innings, hits sixes off the first 5 balls and takes 3 runs off the last ball to retain strike. He repeats this until the 49th over. In the 50th over, he hits six sixes. That's 49*33 + 6*6 = 1,653.
- Ramesh S Mahalingam, ramesh@idealmc.com
 
A single player can score a maximum of 1,653 runs. 33 runs, each in the first 49 overs, hitting sixes off the first 5 balls and taking 3 runs off last ball of each over, thus retaining the strike. In the final over, he hits 36 runs.
- Vinod Mahajan, ?vm1966@gmail.com
 
(The third problem concerned Tom, Dick and Harry, which we needn't go into without running out of tons of papyrus or cartridge ink. Instead to cut a long story short, here's the answer. - MS)
 
Tarry-Tardy-Harry Dept:
The second pair would take 1.78 hours longer to complete the job. Let the time taken by Tom be x hours. The time taken by all three together is x/2 hours. Dick completes the job in x/2 + 8 hours. Harry completes the job in x/2 + 48 hours. This gives 1/(1/x + 1/(x/2 + 8) + 1/(x/2 + 48)) = x/2. Solving this equation, we get x = 10.66 hours. Tom and Harry, therefore, take 8.88 hours to complete the job; Dick and Harry take 10.66 hours to complete the job. Hence, the second pair takes 1.78 hours longer.
- Saifuddin S F Khomosi, ?saif_sfk@hotmail.com
 
ENDGAME(S) 
(To get in touch with ?Mukul, mail him at ?mukul.mindsport@gmail.com)
 

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