Bing Bong Dell
Today, a great celebration will take place on Bell Island because it's the Feast of Coincidus. On this island are a monastery and a nunnery and, at regular intervals (a whole number of minutes apart), the former's bell dongs once. The nunnery bell rings at regular intervals too (different from the intervals of the monastery's bell but also a whole number of minutes). So the island also regularly reverberates with a ding from the nunnery's bell. The Feast takes place whenever the monastery's dong and the nunnery's ding occur at the same moment - and that's exactly what will happen at noon today.
Meanwhile, between consecutive Feasts, the dongs from the monastery and the dings from the nunnery occur alternately and, although the two noises only coincide on Feast days, they do occur a minute apart at some other times. When the bells coincided last time (at noon, a prime number of days ago), this whole island indulged in its celebration of eating and drinking. How many days ago was that?
(The stalemated problem was a remote association test, where you had to find a word that matched with three other given words to make a second sense for each of them. - MS)
(1) Fence, modern, master: POST; (2) Wise, work, tower: CLOCK; (3) Cry, front, ship: BATTLE; (4) Line, fruit, drunk: PUNCH; (5) Child, scan, wash: BRAIN; (6) End, line, lock: DEAD; (7) Mother, after, rate: BIRTH; (8) Lounge, hour, napkin: COCKTAIL; (9) Artist, hatch, route: ESCAPE; (10) Pet, bottom, folk: ROCK.
- Surya Narayanan Krishna Moorthy, firstname.lastname@example.org
(The other problem was: "An hourglass floats inside a narrow tube of water. If the tube is inverted, the hourglass no longer floats till all the sand has fallen into the lower section, even though its buoyancy remains the same since the volume has not changed. Why?" - MS)
When the sand is in the lower part, initially, the metacentre lies above the centre of gravity, causing the hourglass to float. In the event of inverting the tube, the centre of gravity now shifts above, causing the hourglass to sink down. But as the sand gradually falls into the lower half, the centre of gravity slowly starts coming down and, eventually, as the metacentre moves above the centre of gravity, the hourglass starts to float again.
- Saifuddin S F Khomosi, email@example.com
(The third one was: "Why do some sand ripples at the bottom of streams travel upstream?" - MS)
If the addition of sand to the flow during rapid sedimentation is at a rate equal to or greater than the rate of downstream migration of ripples, several trains of ripples are superimposed on each other and seem to climb by generating stratigraphic surfaces tilted in an upstream direction, resulting in climbing ripples travelling upstream.
- Abhay Prakash, firstname.lastname@example.org
(And finally, we have a grouse from a person who agrees with the solution but not with its manner of solving. You're welcome to join in too. - MS)
Refer the puzzle: ''What remainder do you get when you divide 100^100 by 11?" Although the answer '1' is correct, the methodology is not. He says: "When you divide a number by 11, if the sum of all the digits at odd places minus the sum of all the digits at even places is 1, then the remainder will be 1." But in reality, if you divide 1,000 by 11, the remainder will be 10.
- Dr P Gnanaseharan, email@example.com
A shot in a film shows a moving coach pulled by horses. The circumference of the front wheels is 2.5 metres while that of the rear wheels is 2.75 metres. The number of radial arms in each wheel is 12 and the speed of the coach when the shot was taken is 18 kmph. In what direction would the wheels appear to be moving when the scene is projected?
(Mukul can be reached at firstname.lastname@example.org)