One always expects to learn new things when writing an interactive column for years on the trot, but some of those new things can be unexpected. One of the two puzzles below is based on the board game we Indians know as carrom, so I looked for the correct spelling in the Chambers English Dictionary (the big red book or BRB, as crossworders call it) as well as Collins English Dictionary (the online version). I found that Chambers does not have ‘carrom’ at all, only ‘carrom ball’ (from cricket). Collins lists ‘carrom’ as a variant spelling of ‘carom’ (so does Merriam-Webster, but American spellings belong to a different universe). None of the meanings of ‘carom’ in any of the three dictionaries matches the game we are so familiar it.
From other online resources, I found that carrom is indeed the recognised spelling for the game. There is an International Carrom Federation. What I learnt: the game is not widely known in the West. It is widespread only in South Asia and parts of the Middle East. Hopefully, the West will catch up one day, and the game will find its due place in standard dictionaries.
#Puzzle 193.1
In a carrom tournament, the organising club provides the boards and the counters (9 black, 9 white, 1 red), but the contestants are allowed to bring their own strikers, with which they hit the counters. To ensure that some strikers do not provide the user an advantage on account of weight, smoothness etc, the organisers rotate the strikers, so that every player in a group gets to use every striker in that group (including their own) once.
Other rules are tweaked. Four games are played by the four entrants in a group. Each player occupies one side of the board, but there are no partners. Every player is playing for himself or herself, with scoring rules so complex that I dare not explore them in Problematics. The striker rules, however, are easy to understand.
{{/usCountry}}Other rules are tweaked. Four games are played by the four entrants in a group. Each player occupies one side of the board, but there are no partners. Every player is playing for himself or herself, with scoring rules so complex that I dare not explore them in Problematics. The striker rules, however, are easy to understand.
{{/usCountry}}Four games are played by the four players, Ms Singh, Mr Sharma, Ms Srivastava and Mr Sinha. As said earlier, each of them brings his or own striker. Each player uses a different striker in each game. In the fourth and last game, each player uses his or her own game.
In the first game, Mr Sharma uses the red striker. In the second, Ms Sinha uses Ms Srivastava’s black striker. In the third game, Mr Singh uses the white striker and Ms Sinha uses the yellow striker.
Who owns the yellow striker?
#Puzzle 193.2
ab + cd = xy
ab² + cd² = abcd
In the above, a, b, c and d are digits. There is no restriction on whether or not two different variables can represent the same digit. Each one among ab, cd and xy represents a two-digit number, while abcd is a four-digit number. Needless to say, the ab in the first equation is the same as the ab in the second equation, the cd in the first equation is the same as the cd in the second equation, and the same ab and cd appear in abcd.
Only two sets of numbers satisfy both equations simultaneously. Find them.
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 192.1
Hi Kabir,
The motorist will travel a distance of 360 km before returning to his starting point.
He starts with his 8 assistants each carrying 2 + 18 = 20 litres.
In the first leg, they travel for 40 km using 2 litres each. One of the assistants keeps 2 litres for his return journey and distributes the remaining 16 litres among 8 motorists (8 x 2 litres).
In the second leg, they travel a further 40 km using 2 litres each. One of the assistants keeps 4 litres for his return journey and distributes the remaining 14 litres among 7 motorists (7 x 2 litres).
This continues for a total of 8 legs, with one assistant returning after each leg after transferring 2 litres each to the motorists who are still travelling ahead.
After 8 legs, the main motorist has travelled a distance of 320 km while still having 20 litres. This enables him to travel a further 20 x 20 = 400 km. He travels 40 km ahead, and returns 360 km to the starting point. Thus, he travels 360 km and comes back the same distance, a total of 720 km.
— Anil Khanna, Ghaziabad
Kanwarjit Singh adds: Intuitively, once we see that cars will return after every 40 km , the distance travelled by successive cars is 40, 80, 120 , and so on. The 9th term in this series will be 360. The total distance driven by 9 cars will be also be 80, 160… 720 km, totalling 3600 km. The total petrol is 20 x 9 litres, and 3600 km is the distance that can be covered by this much petrol @ 20 km/l.
#Puzzle 192.2
Hi Kabir,
In the first step, the number chosen can be anything from 1 to 9, so the number of matches remaining is from 11 to 19. The sum of the first number and sum of the two digits of the corresponding second number will always be 11. (1 + 1 + 9; 2 + 1 + 8; 3 + 1 + 7; … 9 + 1 + 1.) Therefore, the matchsticks remaining after the second step will always be 20 – 11 = 9. If m is the number of matchsticks remaining at the end, the number of matchsticks in the spectator’s fist will be (9 – m). This is how the magician works it out.
— Yadvendra Somra, Sonipat
Solved both puzzles: Anil Khanna (Ghaziabad), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Yadvendra Somra (Sonipat), Dr Sunita Gupta (Delhi), YK Munjal (Delhi), Professor Anshul Kumar (Delhi), Shishir Gupta (Indore), Sabornee Jana (Mumbai)
Solved #Puzzle 193.2: Vinod Mahajan (Delhi), Ajay Ashok (Delhi)