Problematics | Music old style
This week’s puzzle revisits the record player. What distance does the stylus, or needle, travel along an LP disc?
The way people listen to music has evolved very rapidly. Although the gramophone was before my time, I grew up on the record player and then the tape recorder before the CD and then non-physical media formats arrived, all this in the matter of a few decades. Cassettes are not yet a very distant memory, having been around until at least the 1990s, but I am not sure how many people under the age of 40 or so have ever seen a record player in operation.
The music is recorded on a circular disc of vinyl plastic, with its surface covered with microscopic grooves that spiral inwards towards the centre. As the disc rotates, the music plays when a needle (stylus) comes into contact with these grooves and moves inwards. The needle is mounted on a handle called the tonearm. The other end of the tonearm is attached to a pivot, where it is fixed while the end with the needle moves from the edge of the record towards the centre, carrying the needle along with it
Puzzle #135.1
Record discs come in more than one size, the most common being LP and SP, with each kind defined not only by the disc’s diameter but also by the speed of its rotation. We are not, however, concerned with speed in this puzzle. But size does matter.
Take a hypothetical LP disc, for which I propose dimensions that are plausible. A disc comes with a protective outer ring, called a lead-in groove without any recording. You place the stylus here, letting it slide to the recorded grooves and start playing the music.
Again, the stylus does not move to the actual centre of the disc. It stops at the edge of an inner circle, which carries the manufacturer’s level. The grooves with the music are therefore contained in the space between the lead-in groove and the inner circle.
Take the diameter of an LP disc as 300mm. The lead-in groove has a width of 10mm, and the inner unrecorded circle has a diameter of 100mm. Now play the record from beginning to end, with the needle travelling across all the recorded grooves until it reaches the edge of the inner circle.
What is the total distance travelled by the stylus (needle)?
Puzzle #135.2
Type out an English word describing something that does not exist at any location. Next, place the cursor at a suitable place within the word and press the space bar. You now have a two-word compound describing something that is at this very location at this very moment.
What is the original word (hint: 7 letters) and where does the space bar split it into two?
MAILBOX: LAST WEEK’S ANSWERS
#Puzzle 135.1
Hello Kabir,
I have a doubt about clue #8 in the first puzzle. In other clues the number of places before and after is mentioned. This clue says before but the puzzle does not fit if we take it as just one place before. I tried my best and came up with the solution shown in the table.
Dr Sunita Gupta, Delhi
Dr Gupta, whose answer is correct, got there after addressing her doubts herself. She was not the only one who faced the question she has mentioned; a couple of other readers too mentioned it. To make it clear, if we say that one bowler’s name comes before that of another bowler, it just means before. It can be any number of places before, unless the puzzle explicitly states that it is “one place before” or “two places before”. This confusion among a few readers may be the reason why not everyone got it correct. In future, I shall try and prevent such confusion by qualifying such clues by stating what should ideally be obvious: “somewhere before” or “somewhere after”.
Puzzle #134.2
Hi Kabir,
Let the number of shares held by A and B, initially, be 1.5N and N, respectively. Let the number of shares sold to the new partner by A and B be X and Y, respectively, making everyone's shares equal. Therefore, 1.5N – X = N – Y = X + Y. Solving this gives Y = N/6 and X = 2N/3 or 4N/6. The investment of ₹5 lakh should be shared by A and B in the ratio X:Y, that is, 4:1. Therefore, A gets ₹4 lakh and B gets ₹1 lakh.
Professor Anshul Kumar, Delhi
A few readers misunderstood this puzzle too (adapted from an original by Henry Ernest Dudeney). They assumed that the new partner expanded the business by investing an additional ₹5 lakh, which is not the case. The puzzle stated “payment”, not “investment”, which was intended to convey that the new partner paid this amount to the other two rather than infuse new capital into the business. The size of the business remains as is, ₹15 lakh (since ₹5 lakh is the share one of three equal partners). The other two partners had original investments of ₹9 lakh and ₹6 lakh.
Solved both puzzles: Dr Sunita Gupta (Delhi), Professor Anshul Kumar (Delhi), Yadvendra Somra (Sonipat)
Solved #Puzzle 134.1: Sampath Kumar V (Coimbatore), Sabornee Jana (Mumbai), Ajay Ashok (Delhi), Biren Parmar (Bay Area, California), Aishwarya Rajarathinam (Coimbatore)
Solved #Puzzle 134.2: Vinod Mahajan (Delhi)