Saturday, Feb 04, 2023

# Problematics: Kalam meets Galileo meets Alexander Graham Bell

## This week, meet a whimsical missile and then make 10 celebrity calls

Flight paths the missile can and can’t take (grids courtesy Galileo Educational Network) and the numbers of 10 celebrities (Source: Express illustration)

The Galileo in the headline refers not to the scientist directly but to an institution named after him. The Galileo Educational Network is in the University of Calgary, Canada. Brenda Gladstone, its co-founder and COO, has allowed me to use one of its puzzles, for which I am grateful. This modified version is in memory of A P J Abdul Kalam.

A student aspiring to be a rocket scientist creates a model for a guided missile and tests it in a wide desert. She finds it accelerates @ 10km/minute every minute. At the end of every minute, however, the device changes its direction, turning 90 degrees one way or the other. If it was travelling north, for instance, it turns either east or west when the minute ends. If it was travelling west, it turns either north or south.

The inventor cannot stop its erratic preferences. She can, however, remote-control which way the 90° turn takes place. If the device has just completed a southward minute, she can guide it either east or west, though it must be one of those two directions.

The figure on the top left shows a possible flight path. Every square in the grid is 10km to a side. Note the acceleration: 10km in the first minute, 20km in the second minute, 30km in the third and so on.

It can go on like this forever. The only way to stop this thing is to bring it back to its starting position, under the command of its creator. There is a restriction: a straight line once travelled cannot be intersected again. See the figure that says ‘Not allowed’. The young scientist needs to complete a clean loop, with no lines crisscrossing.

Puzzle#22A: Complete that loop. What is the shortest possible travel time?

What you wrote

We travelled to Kepler-452b last week with two puzzles.  Here are your answers.

Dear Kabir, in Puzzle#21A, the man covers a circular arc on the ground with radius R, say. So the distance covered by his feet will be 2πR. The head will also cover a circular arc, with radius say (R + r). Therefore, the extra distance covered would be 2πr. Here, r = 3m; therefore distance = 2π × 3/1000 = 0.0188 km.

— Anirudha Hulsurkar (B Tech, IIT Roorkee)

***

Dear Kabir, I solved Puzzle#21B with a set of two equations. The mystery factor is planet diameter/moon diameter, hence the measurement is relative to the size of the moon. A value of 1 would mean we are the reference, i.e. moon. The unknown value for Kepler-452b is between 5.8 and 5.9. Never read Asimov. Solving equations is more fun.

— Neha Awasthi (Goettingen, Germany)

Solved both puzzles: Anirudha (above), Neha (above), Sanjay Gupta (New Delhi), Sathya Prakash (New Jersey)

Solved first puzzle: Phani Bhushan Tholeti (Synaptics, Hyderabad), Sampath Kumar V (IIM-K alumnus). Sampath solved 1½ puzzles; he calculated the ‘mystery factor’ for Kepler-452b at 5.86 but didn’t show us the connection to the moon.

Telephone scientists

August 2 was the death anniversary of Alexander Graham Bell as well as the birth anniversary of his rival Elisha Gray. Those two fought bitterly over who actually invented the telephone.

Go back to the main illustration and look at the telephone dial. Once upon a time, the digits came with letters as a memory aid. For example, if someone might struggle to remember the sequence 3-2-6 but could easily remember to dial the word H-E-R.

In early mobile phones, the small keypad used a different correspondence between digits and letters. I have provided both a telephone dial and a mobile keypad for reference. I have also chosen the names of 10 celebrities and converted the letters into digits.

The hyphens stand for the separation between first and last names. For the first fictional character (STD), the first word is actually a designation, abbreviated. For the last fictional character (mobile), one of the only three women in this set, the first word is a salutation.