# Hint: A for Apple… and Logic Always Wins!

Published: 23rd February 2014 06:00 AM  |   Last Updated: 21st February 2014 12:36 PM   |  A+A-

W Sylvester,  Altaf Ahmed and Krishna have inquired if it’s okay to send in puzzles to be run here. I had already mentioned in an earlier column that you’re welcome to do so whenever you want and if they’re good enough to get other people’s right brain ticking then we’ll run them. And of course I’d be more than happy for this uninvited manna. There’s only one rider though and a very important one: if you’re like me and pinch problems from anything your soapy hands can hold on to without slipping, then PLEASE acknowledge your source so that you and I don’t end up doing copyright time together in some godforsaken slammer. (Oh and send in the answers also, or I’m dead meat!)

And, as usual, meanwhile, check out this list of 26 words/phrases. ‘Orses, dawn, yourself, payment, peron, vescence, police, retirement, an eye, e. Chaucer , sutherland, leather, sis, sir, population, relief, tickets, conan doyle, williams, mation, ia, la france, a match?, breakfast, mistress, marx brothers.

What’s the logical connection between all of them?

Throughput

The problem concerned a certain Juliette and her sister Lucille who lived together in Montreux and somehow still managed to intricate themselves into a riddle which got solved in India. Watch again how:

If Juliette runs to the point 30 metres away (from the point she left the road) towards Montreux, she will make it. Another point where she can catch the bus is 50/3 metres on the same segment. Though Lucille is only one metre farther, she is too far  away to be able to catch the bus. This is, of course, assuming, as usual, that the bus and Juliette have no dimensions, that Juliette takes no time to board the bus and that in the hurry, the two sisters do not fall one on top of the other. If Lucille runs a little faster, say, 51% (instead of 50%) as fast as the bus, she too might get in. -- Rajagopalan K T, ktremail@gmail.com

The only way for the sisters to catch the moving bus on the main stretch of the road would be to run diagonally across the field (say X metres) in the same direction as the bus (i.e. if the bus is to their right, they run diagonally left and vice versa); in which case the bus would have covered a distance equal to 70 + say ‘Y’ metres at the time either of the sisters meets the bus.. It can be noted that (70 + Y) equals twice the distance ‘X’ travelled by the sisters since the bus is moving twice as fast as the sisters. Consequently, the situation can be reduced to a right angled triangle with sides 40 (in the case of Juliette), Y and hypotenuse X. In the case of the second sister the third side is 41. Solving for Y, we get Y = 32.8 m and 16.79 m (approx) for case 1. However, the second sister Lucille would not be able to catch the bus for the given conditions (since Y yields a complex number). Hence, the first sister Juliette could catch the bus if she ran diagonally across the field so as to meet the bus at 16.79 and 32.8 m respectively from the point where they left the road. -- SBNVTL, sbn_vtl@yahoo.co.in

The other question was: “Why are the rear wheels of a tractor sometimes also filled with a fluid instead of air?”

The pull developed by a tractor depends not only on the force that the engine transmits to the big rear drive wheels but also on the load

on these wheels.

If the axle load is too small, the wheels could slip and fail to grip the ground. Thus to increase the load and press the wheels more firmly against the ground, ballast weights are sometimes provided in the rear of the vehicle. Other times, the wheels are filled with water instead of air. S Ashutosh, Suruli92@hotmail.com

Here are three fun ones with two answers so you can try most on others. (1) In a 12-hour period from noon to midnight how many times does the minute hand overtake the hour hand? (10 times) (2) If a bottle and cap together cost 10 rupees fifty paise and the bottle costs 10 rupees more than the cap, then how much does the cap cost? (3) A frog is at the bottom of a 30 foot well. Each hour he climbs three feet and slips back two feet. How many hours does it take him to get out? (28 hours)

— Sharma is a scriptwriter and former editor of Science Today magazine.

(mukul.mindsport@gmail.com)

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