Problematics | Siblings who bowl and bat
Four brother-sister pairs play some matches and score some runs. Who is whose sibling, and who scores how much in how many matches?
Finding puzzles week after week does not mean creating new ones all the time. As I have done on several previous occasions, I am borrowing this week from England’s greatest puzzler, Henry Ernest Dudeney, who enthralled fans about a century ago.
We had run a somewhat similar puzzle some months ago, so regular readers may find it familiar. In fact, such puzzles should ideally appear every now and then, if there were enough of them to recycle. I have done away with Dudeney’s original story, which wouldn’t work in today’s age and which anyway is in the public domain. So here comes the old wine in my new bottle.
Puzzle #130.1
Four pairs of siblings, a brother and a sister in each pair, go to the same school. In alphabetical order, the boys are called Arjun, Bharat, Chandan and Dinesh, and the girls are Esha, Gauri, Hema and Kamala. Each of the eight plays as a bowler in the boys’ or girls’ team of their school, but not all of them is a good batter. At the end of the season, they compare the runs they have scored.
1. Every bowler has scored, on average, as many runs per match as the total number of matches he or she has played. In other words, if the bowler has played x matches, he or she has scored a total of x² runs.
2. Every brother has played twice as many matches as his sister.
3. Arjun has played three matches more than Esha.
4. Gauri has played two matches more than Hema.
5. Bharat has scored 76 runs more than Chandan.
6. Dinesh has scored 48 runs more than Hema.
Who is whose sibling, and who played how many matches and scored how many runs?
Puzzle #130.2
Two couples with the surnames Chatterjee and Das get together for lunch, with tw o persons seated on either side of the table. We know the professions of two of the four: one is a graffiti artist and another is a sound recordist.
1. The graffiti artist and the sound recordist are seated on the same side of the table.
2. Mr Chatterjee and Ms Das are seated on opposite sides of the table, facing each other directly (not diagonally).
3. Mr Das and the spouse of the graffiti artist are seated on opposite sides of the table, each diagonally across the other.
Whose profession do we know for certain?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 129.1
Hi Kabir,
It is observed that:
Superman's name has an R, but no B. Statement #1 has Rs, but no B
Batman's name has a B, but no R. Statement #3 has Bs but no R
Robin's name has an R and a B. Statement #2 has both ₹and Bs
So, Statement #1 was made by Superman, Statement #2 by Robin, and Statement #3 by Batman.
Superman has stated that one among him and Robin is a liar and the other is truthful.
Robin has stated that either Batman and he both are liars or both are truthful.
Batman has stated that at least one among Superman and Robin is truthful.
If Superman is truthful, his statement means Robin must be a liar since only one of the two is truthful. If Superman is a liar, his statement is false, and by implication, Robin must also be a liar since the number of liars between the two of them is not one. Thus Robin is a liar in any case.
As Robin is a liar, his statement is false, and by implication, Batman must be truthful since both can't be liars. According to Batman's statement (which is true), at least one among Superman and Robin is truthful. Since Robin is a liar, Superman must be truthful.
Conclusion: Superman (Statement #1) and Batman (#Statement #3) are truthful while Robin (Statement #2) is a liar.
— Professor Anshul Kumar, Delhi
Puzzle #129.2
The longest dictionary words using only the letters from the top row of a keyboard/keypad:
TYPEWRITER, PERPETUITY, REPERTOIRE, PROPRIETOR (10 letters each)
— Many readers
TYPEWRITTEN, PROPRIETARY, RUPTUREWORT, PROTEROTYPE (11 letters each)
— Shishir Gupta (Indore), Y K Munjal (Delhi), Ajay Ashok (Delhi), Sanjay Gupta (Delhi), Dr Sunita Gupta (Delhi)
Solved both puzzles: Professor Anshul Kumar (Delhi), Shishir Gupta (Indore), Sanjay Gupta (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Yadvendra Somra (Sonipat), Amarpreet (Delhi), Aishwarya Rajarathinam (Coimbatore), Sabornee Jana (Mumbai)
Solved Puzzle #129.2: Y K Munjal (Delhi), Ajay Ashok (Delhi), Dr Sunita Gupta (Delhi), Vinod Mahajan (Delhi), Anil Khanna (Ghaziabad)