Problematics | Reluctant recruits go to war

As an occasional setter of cryptic crosswords, I have sometimes composed clues and then forgotten about them. As a result, when I come across those clues after some months, I sometimes struggle to solve them myself.

As it turns out, this can happen with mathematical puzzles too. Among my old clippings from the early 1990s, I found a puzzle that I have no recollection of creating or adapting from an existing original. From a later clipping, I found that a number of readers had got it wrong. For the solution, I had to refer to readers’ responses and my own observations made over three decades ago.

The following is an entirely new version. Do let me know what you think of it.

#Puzzle 78.1

Once upon a time, many centuries ago, two tribes were locked in a one-sided yet endless war. The reason it was one-sided was that the WinWin tribe always had plenty of volunteers ready to go to battle. And the reason it was endless was that the chief of the LoseLose tribe, although always short of recruits, was still refusing to surrender.

One day, smarting after yet another defeat suffered by his outnumbered soldiers, the LoseLose chief decided that the only way to get more recruits was by paying their families. He shrewdly decided to reward the women heading these families, for he guessed they would have a prevailing influence on who would enlist for battle.

1. Every woman heading a family, coincidentally, had two children: one son and one daughter.

2. If she sent her husband to war, she would earn 750 bags of rice.

3. If she sent her son, she would earn 1,000 bags of rice.

4. If she sent her daughter, she would again earn 1,000 bags of rice.

5. Two-thirds of all family heads sent their husbands.

6. Three-fourths of all family heads sent their son.

7. Four-fifths of all family heads sent their daughter.

8. At least 52 women heading a family sent all three: her husband, son, and daughter.

How many bags of rice were paid out in total?

#Puzzle 78.2

Unscramble these anagrams to get the names of five retired male cricketers (two from England, one each from India, South Africa and Sri Lanka).

MAILBOX: LAST WEEK’S SOLVERS

#Puzzle 77.1

Hi Kabir,

The solution is shown in the table above. Working it out from a blank table is fairly straightforward. Barring clues 4 and 5, the rest will fit easily into the grid. Clue 4 can give two possibilities, but looking at the filled table, one of the two possibilities can be eliminated very quickly.

In the crossword, the language SANTHALI can also be spelt SANTALI. If one tries to solve #77.2 with SANTALI as the spelling, then it is impossible to solve. In case any reader contacts you, then you can inform them that the puzzle is constructed with SANTHALI as the spelling.

— Akshay Bakhai, Mumbai

Indeed, Akshay, one other reader did use SANTALI as the spelling, after which I alerted them that we are going with SANTHALI. Some other readers, on the other hand, made a point about ODIA/ORIYA. I built the grid using ODIA, which is the spelling used by the Odisha government. However, given that I did not specify the spelling, ORIA works too. Even those who tried to fit in the five letters of ORIYA, although only four cells were available, are being counted as correct. The following solution uses the spelling ODIA.

#Puzzle 77.2

Solved both puzzles: Akshay Bakhai (Mumbai), Dr Sunita Gupta (Delhi), Sampath Kumar V (Coimbatore), Sundarraj C (Bengaluru), Charvi Brajpuriya (Faridabad), Group Captain RK Shrivastava (retired; Delhi), Ajay Ashok (Mumbai), Sanjay S (Coimbatore), Professor Anshul Kumar (Delhi), Shishir Gupta (Indore), Aafiya (Coimbatore), Amarpreet (Delhi), Yadvendra Somra (Sonipat)

Solved Puzzle #77.1: Vishnuvardhan (Sydney), Kanwarjit Singh (Chief Commissioner of Income Tax, retired; Delhi), Anil Khanna (Dy DG, retired, Ministry of Defence; Ghaziabad)

Solved Puzzle #77.2: Jaikumar Inder Bhatia & Disha Bhatia (Ulhasnagar, Thane)

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