Question #1: Which man drinks diet soda? Question #2: Which man owns a spider monkey? Given that . . . There are five houses and that in each house lives a man of a certain nationality who has his favourite drink, his favourite game and his own unusual pet. And furthermore . . .
(1) There are five houses in a row, each having a different colour; (2) The Englishman lives in the red house; (3) The green house is to the right of the white house; (4) The Italian owns a guppy; (5) Lemonade is drunk in the green house; (6) The Swede drinks coffee; (7) The man who plays backgammon owns a toad; (8) The man who plays racquetball lives in the yellow house; (9) The man in the middle house drinks milk; (10) The Russian lives in the first house; (11) The man who owns the camel lives next to the man who plays quoits; (12) The man who owns the rat lives next to the man who plays racquetball; (13) The man who plays solitaire drinks herb tea; (14) The American plays charades; (15) The Russian lives next to the blue house.
THROUGHPUT
(The ageing problem was: “For the first half of the journey you drive at 20 kmph. Then you realise you’re going to be late. So you decide to increase your speed so the overall average speed for the whole journey will be 40 kmph. How fast do you have to drive for the remaining part?”)
When half the distance is covered at a particular speed, to get double the average speed for the total distance is not possible. This can be easily realised by taking an example. Suppose total distance is 40 km. Then total average speed 40 km/hr means entire distance has to be covered in one hour. But if half distance is travelled at 20 km/hr means to cover 20 km itself will take one hour. That means balance 20 km has to be covered in 0 time. This is impossible. -- Parameswaraiah Ganeshaiah, parameswaraiah@gmail.com
(The second one was: “A film shot shows a moving coach with front wheel circumference 2.5 m and rear 2.75 m. Spokes in each wheel are 12 and the speed of the coach is 18 kmph. In what direction would the wheels appear to be moving when projected?”)
Front wheels will look stationary and rear wheels would rotate in the reverse direction. This is because every second we can see 24 radial arms per second in the first wheel. But in the second wheel we can see 21 9/11 radial arms only per second. -- P Ganesh Ram, 1969ganram@gmail.com
Motion picture cameras conventionally film at 24 frames per second. The speed of the coach when the shot was taken = 18 kmph = 5 mps.
The distance travelled by the front wheel in one second = 2.5 meters. Thus the front wheel had completed two revolutions in one second. Similarly, the number of revolutions of the rear wheel per second = (5)/(2.75) = 1.8182 (approx). The number of spokes in each wheel is 12. Because the number of times the front wheel rotates per second is a factor of 24 and 12, the front wheel will appear to be stationary. The rear wheel, which is moving at 1.8182 or a little less than two revolutions per second, will fall a little further behind in each successive frame and therefore will appear to be rotating backwards. -- Narayana Murty Karri, k_n_murty@yahoo.com
(And, finally, we have a response from a responsible co-responder to reconsider.)
This is about Dr Gnanaseharan’s comment on methodology of arriving at the remainder in 100^100/11 and your invitation to join in. Dr Gnanaseharan is right in his comment. The divisibility test of 11 that the difference in alternating sums from left to right should be either 0 or divisible by 11 does not necessarily mean that if the difference in alternating sums is 1 then the remainder is 1, as disproved for 1000. An even power of 10 when divided by 11 will leave 1 as remainder. An odd power of 10 when divided by 11 will give 10 as remainder. As 100 is an even power of 10, any power of 100 when divided by 11 will give 1 as remainder. QED. -- Abhay Prakash, abhayprakash@hotmail.com
BUT GOOGLE THIS NOW
1. What are the next four numbers in the series 12, 1, 1, 1, 2, 1, 3, ?, ?, ?, ?
2. A cube of butter is sliced five times by a butter knife. Into how many pieces at most can the cube of butter thereby be divided if each knife stroke is perfectly straight (ie, planar) and the pieces of butter are never rearranged?
— Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)