A Good Question

The following story of a king and his wise jester may or may not be germane to the problem that follows but it's fun.

E4
The following story of a king and his wise jester may or may not be germane to the problem that follows but it's fun. One day a scholar came to the court of king Akbar and challenged Birbal to answer his questions and thus prove that he was as clever as people said he was. He asked Birbal: "Would you prefer to answer a hundred easy questions or just a single difficult one?" Both the king and Birbal had had a diffi-cult day and were impatient to leave. "Ask me one difficult question," said Birbal. "Well, then tell me," said the man, "which came first, the chicken or the egg?" "The chicken," replied Birbal, confidently. "How do you know?" asked the scholar, with a note of triumph.
Birbal said, "You said you'd ask me only one difficult question, so why are you asking two now?" Then he and the king walked away leaving the scholar gaping.
"Find me the smallest integer that consists of only digits 3, 5 and 7," said another king to his jester. "How simple," said the jester. "But," continued the king, "this number should be divisible by 3, 5 and 7." The jester suddenly looked serious. "And finally," remarked the king, "the sum of the digits of this number should be divisible by 3, 5 and 7." The jester appeared miserable. "Solution by tomorrow morning," added the king. "Or you must marry my widowed mother-in-law." Unlike Birbal, this jester was crushed.
DEAR MS
(The problem concerned a mathematical card trick with an unasked question which, I'm happy to say, has been successively unmasked thereafter. - MS
Face-Value-Dept:
This trick works on arithmetic. First you deal 12 cards from the shuffled pack. Then four cards with face values, say a, b, c and d are chosen from them. After that 10 - a cards are placed on a, 10 - b on b, 10 - c on c and 10 - d on d, in effect removing 40 - (a + b + c = d) cards and leaving 52 - (12 + 40 - (a + b + c = d)) = (a + b + c + d) cards in the pack. Therefore, when the third person turns over the (a + b + c + d)th card, it will be the 52^nd card, which was at the bottom of the pack after it was shuffled and placed on the table. Now, the magic lies in unobtrusively observing the bottom card and writing it on a piece of paper.

• Balagopalan Nair, balagopalannair@gmail.com

(Regarding the problem of distance from one mountain to another.)
Going-From-A-To-B-Dept:
First, find the average speed of the car as it travels downhill (72 kmph) and uphill (56 kmph). The average speed will be 63 kmph (not arithmetic mean). Thus the average speed for entire journey from point A to B and return journey from B to A will be 63 kmph and time taken is 8 2/3 hours. Total distance of return trip = 63*8 2/3 = 546 kms. Distance between A and B = 546/2 = 273 kms. The time difference of 40 minutes is due to the fact that distance from A to Plain is more than distance from Plain to B (10.5 kms).

• Tijender Kumar Gupta, tijender.gupta@gmail.com (Yes Gary Miller, garyr_miller@hotmail.com, you got it right too - MS)   

(And lastly, the unpublished response to the logic question posted a couple of weeks ago can now be run. - MS)
Workers-Of-The-World-Dept:
Shucks, the whole thing sucks. Nevertheless, here goes the saga: 1. Bottle Washer (A): 18 bucks 90 sucks; 2. Door Shutter (B): 20 bucks; 3. Door Opener (C): 12 bucks 10 sucks; 4. Doorknob Polisher (D): 11 bucks; 5. Welfare Officer (E): 12 bucks.

• Saifuddin S F Khomosi, saif_sfk@hotmail.com

ENDGAME(S)

1. If an hourglass with all the sand in the upper half is placed in water, it sinks to the bottom. But as sand gradually falls into the lower half, the hourglass moves upwards. Why?
2. Some tribal "doctors" treat snakebites by sucking out blood from the wound. If blood groups are so important during transfusions, then why is it that nothing happens to the person when it's being sucked out?

(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)

• Mindsport