Friday, June 18, 2021

# Problematics: What 4-digit number connects Modi, Sharif, Xi, Cameron, Obama and Hasina?

## Four variables always add up to 4,030 for each of these six leaders; why must it be so?

Identify the Oscar winner, explain the identical sum, move the matches, rearrange a few symbols and weigh the glasses. (Source: Express illustration by Kabir Firaque)

Every week, it has become a trend for readers to point out that my puzzles are either too easy or too tough. For those calling for easier ones, let’s see if a little more variety than usual can give every reader something (s)he is comfortable with. Call these ‘Five Easy Pieces’, after a Jack Nicholson movie of 1970.

Puzzle#14A (i): In my illustration, begin with the table at the top centre. What’s common to the leaders listed? (a) All of them assumed office in the first half of a calendar year, meaning their governments have already had their 2015 anniversaries; (b) all of them were born in the second half of a calendar year, meaning the “next birthday” will be in 2015, with Xi’s 62nd coming up next week; (c) the total of the four variables is equal for each leader. Why must it be so? Coincidence, mathematics, or destiny?

#14A(ii): One step clockwise takes us to the coin inside the wineglass. Move exactly two matches to new positions so that the four matches together form the glass once again, but with the coin outside it now. This is a vintage puzzle, not mine, but I don’t know who the original creator is.

#14A(iii): From the section of the periodic table shown, select the symbols of four elements in consecutive atomic order. Take a fifth symbol, some places ahead in the table. That will give you six letters from five symbols. Rearrange these six letters to form the full name of one of those five elements.

#14A(iv): One step farther clockwise takes us to the two glasses of water. One, with just water, is full to the brim. In the identical second glass floats a piece of wood, so that the water again reaches the brim. All components included, which glass is heavier? Partha Ghose and Dipankar Home ask this question in their brilliant science book, ‘Riddles in Your Teacup’ (Rupa, 1990).

My fifth puzzle, illustrated on the far left, is about an Academy Award. That will come up after we have read your letters.

What you wrote
Last week’s family planning puzzle can be solved in all sorts of complicated ways, with the associated danger of getting all mixed up. Sathya Prakash chooses the simplest way, which is with an illustrative example.

In Puzzle#13A, the scheme will not work. Assuming that the couples have a child each year (assuming no twins) and there is an equal probability of a boy or a girl, then the couples who can have a child every subsequent year would be diminishing by 50%. So the total of the boys and girls at the end of each year would be the same. The illustration assumes 100 couples. The number of boys and girls at the end of each year remains the same.
Sathya Prakash (software developer, New Jersey)
***
Dear Kabir, The scheme as envisaged will have no extra or added benefit – it will not improve upon the outcome that will come from just natural untampered birth of kids. This scheme will not lead to any “beti badhao” more than normal. Yes, it will help in fact with family planning. But the more important need of the hour probably is “beti bachao” – betiyan will then apne aap badho!
Vivek Jalan (founder, Customate Systems; JMD, Mahalaxmi Seamless Ltd)

***
In Puzzle#13B, the following are the only eight sequences possible, if we respect the rules — BBGGBB; BBGGGBB; BGGBB; BGGGBB; GBB; GBG; GGBB; GGGBB. It can be seen that in six of the eight cases,boys are equal to or more than girls. Only in two cases do girls outnumber boys. But, since it is mentioned that the school takes the maximum number of people possible, it is case 2 (BBGGGBB), where there are 4 boys and 3 girls.
Sampath Kumar V (IIM Kozhikode alumnus)
Sanjay Gupta (New Delhi)

Solved both puzzles: Sathya, Sampath, Sanjay Gupta (New Delhi) and M Natrajan (IIM Calcutta alumnus).
Solved Puzzle #13A: Vivek, Tushar Menon (masters student, NTU Singapore) and Jaysun Antony Alumkal (coordinator, academic committee, IIM Raipur)
Solved Puzzle #13B: Bindia George (IT engineer, Kochi)

(a) I am an actress. In the 1950s, I played the title role in the Broadway version of a French play. But when Hollywood filmed the play, they selected another actress, who is half French. The film, a musical, swept the Oscars.
(b) In the 1960s, it was my turn to snatch another actress’s role. This was a British play and the stage actress was English. I am half English and bagged the Hollywood role. This film, another musical, swept the Oscars but I missed out again. I wasn’t even nominated, because my singing voice had been dubbed by a professional singer.
(c) Adding insult to injury, that year’s Best Actress was the same English actress whose role I had snatched. She won the award for yet another musical movie.
(d) I died more than 20 years ago, in my 60s. The half-French actress is in her 80s today; the English actress will be 80 this year.

Puzzle#14B: Whom am I?