Problematics | Five parties, five defections

Meet five politicians who switch parties ahead of the elections. Which member came from which party, and who went where?

There are times when one must give in to temptation and eat one’s words. Just a couple of weeks ago, I had asserted that there was no reason to make our puzzles topical. “Just because this is election season does not mean we should scratch our heads over an Einstein puzzle about which candidate driving which car is being fielded from which seat by which party,” you may remember me having written. Those are the words I take back now, the temptation being too high.

Here’s an Einstein puzzle about members from different parties switching sides ahead of the elections. (Shutterstock) (Shutterstock)

So, here’s an Einstein puzzle about members from different parties switching sides ahead of the elections. There are, however, precautions one must take. We cannot name real people and real parties for obvious reasons.

In the following puzzle, the five parties are the Heavyweights (HW) who are seen as favourites, the Old Timers (OT) who are no longer in power, the Regional Giants (RG) who are lions in their own den, the New Kids (NK) who rule a couple of states, and the Also-Rans (AR) who never win enough seats to make any impact.

For simplicity, we can call the party members Crossover, Defector, Opportunist, Rebel, and Turncoat.

#Puzzle 85.1

This is much easier than some of our earlier Einstein puzzles, but here are your clues:

2. Each party loses one member among Crossover, Defector, Opportunist, Rebel, and Turncoat to defection, and gains another member from the same set of five people.

3. The original OT member goes to HW.

4. Defector leaves HW to join another party.

5. Rebel joins AR, Opportunist joins RG, and Turncoat joins OT.

6. The person leaving AR is not joining RG.

Who has left which party to join which party? Please send your answers in tabular form.

#Puzzle 85.2

The first time I came across this puzzle was in the form of a short story by Enid Blyton, more than 45 years ago. Since then, I have seen various other versions, the only change being in the numbers.

In the days before cigarettes were filter-tipped, people would throw away the butts with some tobacco still left in them. A miser, who doesn’t want to spend on cigarettes, picks up butts from other people’s ashtrays. He does buy lots of cigarette paper. From the collected butts, he extracts the tobacco and rolls them into new cigarettes using his paper. The tobacco from six butts makes one new cigarette. If he collects 216 butts, how many cigarettes will he be able to smoke?

MAILBOX: LAST WEEK’S ANSWERS

#Puzzle 84.1

Dear Kabir,

Victor and Victoria played a total of 9 games, in which Victor won ₹1 in the first game and ₹4 in the third game (Total ₹5). Victoria won ₹2, ₹8, ₹16, ₹32, ₹64, ₹128 & ₹256 in the second, fourth, fifth, sixth, seventh eighth and ninth games (total ₹506). So after the ninth game, Victoria had a gain of ₹501 over Victor.

— Group Captain RK Shrivastava, Delhi

This was indeed the solution I had in mind, and many readers including Group Captain Shrivastava have given this very answer. However, as it turns out, the solution is not unique, as noted by Professor Anshul Kumar and Akshay Bakhai. In fact, there may be an infinite number of solutions.

Solution 84.1

Hi Kabir,

The possible solutions are summarised in the table. In all these solutions, the results of the first 8 games are identical. After that, Victor loses the very next game or has a winning spree before losing the final game.

— Professor Anshul Kumar, Delhi

#Puzzle 84.2

If the actual runs scored by the East, West and South captains are E, W and S, their actual grand total is E + W + S. We are given that

E + 2W + 4S = 911; and

7E + 5W + S = 1616

Multiplying the first equation by 2 and adding the second, we get:

9E + 9W + 9S = 3438

or, E + W + S = 382

— Kanwarjit Singh, Chief Commissioner of Income Tax (retired)

Solved both puzzles: Group Captain RK Shrivastava (retired, Delhi), Professor Anshul Kumar (Delhi), Akshay Bakhai (Mumbai), Kanwarjit Singh (Chief Commissioner of Income Tax, retired), Sanjay S (Coimbatore), Dr Sunita Gupta (Delhi), Shishir Gupta (Indore)

Solved #Puzzle 84.2: Shruti M Sethi (Ludhiana), Yadvendra Somra (Sonipat), YK Munjal (Delhi)

Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com