Ever notice how uber clever answers have this tendency sometimes to blow up all over your face? In fact mine frequently looks like I’ve just sneezed into an ashtray from up close. Happened in fact only the other day when I was going through an old book of puzzles when the following one collided with my eyes. A gramophone record (those old round hard plastic things, remember, that made music and stuff when suitably rotated on a turntable?) has, I was informed by the printed page, a total diameter of 12 inches. The recording itself leaves an outer margin of 1 inch while the diameter of the unused centre of the record is 4 inches. There are an average of 90 grooves to the inch. And the question was: how far does the needle travel when the record is played?
Hah! I told myself, you can’t fool me with all this outer margin mumbo-jumbo because the number of grooves per inch has nothing to do with it. The needle doesn’t travel around the record, it’s the record that turns. The needle is stationary except for the movement towards the centre of the record. That means it just travels 6 - (2 + 1) = 3 inches! Howling with shameless glee I turned to the answers section at the back of the book only to have another ashtray sneeze right back into my face. I was wrong!
But I’m not going to tell you why my NEW! IMPROVED! ans was incorrect. You tell me.
This is regarding the nieces and nephews problem. Using simple simultaneous equations with four variables and four equations the ages are: Johnny: 3 years 6 months; Anne: 1 years 9 months; Nadine: 5 years 3 months; Alexis: 10 years 6 months; Libby: 21 years (as given). BTW, those who grew up on Dynasty will remember Alexis as a feminine name! -- J R K Rao, firstname.lastname@example.org
(Among others who got it right are: Rajagopalan K T, email@example.com; Dr Vallish B N, firstname.lastname@example.org; Apsalan V A, email@example.com; Arpan, firstname.lastname@example.org and Dr P Gnanaseharan, email@example.com. -- MS)
(The other problem was: “You have two plastic cubes on your desk. Every day you arrange both cubes so that the front faces show the current day of the month. What numbers are on the faces of the cubes to allow this?”)
The numbers on the faces of the two cubes could be: Cube A: 0, 1, 2, 7, 8, 9; Cube B: 1, 2, 3, 4, 5, 6. All the dates can be shown on the two cubes, except for the 7th, 8th and 9th which would require only one cube. So the other cube could be hidden away somewhere on those three dates! -- Murali Kumar, firstname.lastname@example.org (That’s technically correct MK but not a very elegant solution as the following one -- MS)
The first cube should be marked 0, 1, 2, 4, 5, 9 (9 should be marked in such way that it will read as 6 when turned upside down!). The second cube should be marked 0, 1, 2, 3, 7, 8. -- Rajamani. A R, email@example.com
The problem should perhaps read “current date” instead of “current day”. In any case, the answer is: Cube A: 0, 1, 2, 3, 4, 5; Cube B: 0, 1, 2, 6, 7, 8. Number 6 can also be used as 9 by reversing it. -- R Viswanathan, firstname.lastname@example.org
(Other early birders who got it too are: Narayana Murty Karri, email@example.com; Suresh Pai, firstname.lastname@example.org; Baru P V, email@example.com; Rajagopalan K T, firstname.lastname@example.org and Dhruv Narayan, email@example.com. -- MS)
(The third problem was: “Take oil and water in a beaker. The oil floats in a separate layer above the water. In which direction should one accelerate the beaker to mix the oil and water (to make an emulsion?)
The acceleration required is vertical circular motion. Example: Keep the beaker in a giant wheel. The upward and downward motions give different inertia to oil and water as their densities are different and hence they undergo differential up and down movement which will facilitate vertical mixing. -- Prof A Jayaraman, firstname.lastname@example.org
BUT GOOGLE THIS NOW:
1. A number of cats killed 1,111,111 mice, every cat being responsible for an equal number of mice. As there were more mice killed by each cat than there were cats, how many cats were there in all?
2. If Earth’s atmospheric pressure was only one-tenth of what it is now, then why wouldn’t a horse driven carriage driver’s whip wield the same power of authority over the horse?
Sharma is a scriptwriter and former editor of Science Today magazine.