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Problematics | How to place your railway seat
This week’s puzzle examine the layout of a three-tier train coach and distribute more than 1000 berries into six unequal shares.
Train coaches come in different configurations. Many more people travel AC now than in the old days, but an even higher number uses the three-tier coach. Such coaches have not changed their layout over the decades. Which is why I am reviving a very simple puzzle I had set before readers of another newspaper 10 years ago.
#Puzzle 175.1
A typical three-tier coach has 72 seats spread across a number of compartments. My illustration above shows the seats 1-16 after you board the coach from the left door and move right.
If you buy a reserved seat, the ticket and the Railways website not only state the seat number but also specify whether it is upper, middle, lower, side upper, or side lower. If you don’t get a reservation immediately and your seat is confirmed later, the ticket will not mention the seat (or its position), which will appear only on the updated list.
Meet a family that has not got a reservation. One hour before the train is due to leave, the updated list is placed on the notice board. With a crowd gathering around the board, the family sends its young boy to push his way through and check the numbers.
Son: All four seats confirmed.
Father: Which numbers?
Son: You are at 17.
Father: Upper or lower?
But the boy is already looking at the other seats.
Daughter (who is with her parents): 17 is lower, Father.
Meanwhile, son: Mother’s seat is 27.
Mother: Upper or lower?
Daughter: Don’t ask him, Mother. 27 is upper.
The son comes back and tells his sister, “Your seat is 20, mine is 21.”
Are the siblings in upper, lower, middle or side seats? How does the girl work it out each time?
#Puzzle 175.2
Six children raid a garden and collect more than 1000 berries. The amounts collected are unequal. If Arjun gives 2 of his berries to Bhagat, the two boys will have equal shares, with each number being equal to the square root of Charulata’s share. Charulata has a lot: the square root of her share is twice Dilip’s share, and equal to the square of Esa’s share, the latter’s share being the smallest. Farida has twice as many berries as the square root of Charulata’s share. The total number of berries is less than 1,500. All these equations come from Henry Dudeney, whose original version dealt with money and not berries.
How much is whose share?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 174.1
Hi Kabir,
The hidden word is TALL. It matches the following results:
LOSA: OO. L, A at wrong positions. Does not contain O, S
ASCT: OO. A, T at wrong positions. Does not contain S, C
CTLO: OX. L at the right position, T at a wrong position. Does not contain C, O
TLOS: XO. T at the right position, L at a wrong position. Does not contain O, S
OACT: XO. A at the right position, T at a wrong position. Does not contain O, C
Thus, the hidden word contains TAL at the right positions and as it is a four-letter word, and a letter can be used twice, the word satisfying all the conditions must be TALL.
— Anil Khanna, Ghaziabad
***
Hello Kabir,
I recalled my childhood when we used to play this game with coloured pegs, not words. The hidden word is TALL.
— Dr Sunita Gupta, New Delhi
#Puzzle 174.2
Half the shares of Blackbeard and Redbeard when added to Bluebeard’s share make it 3 times Bluebeard’s original. In other words, the total of these two halves is twice Bluebeard’s share. If the entire shares of the other two were added, it would have been 5 times Bluebeard’s original share, and this total is 1000. Therefore, Bluebeard’s share is 200
Similarly, half the shares of Bluebeard and Redbeard increase Blackbeard’s share by one-and-a-half times. This means their total is just half of Blackbeard’s share. If the entire halves were added, Blackbeard’s total would have doubled to 1000. Hence Blackbeard ‘s share is 500.
Thus the shares are Bluebeard = 200, Blackbeard = 500, Redbeard = 300. Bluebeard’s dream would give him 200 + 150 + 250 = 600, which is 3 times the original share. Blackbeard’s dream would give him 100 + 500 + 150 = 750, which is one-and-a-half times his original share.
— Kanwarjit Singh, Chief Commissioner of Income tax, retired
Solved both puzzles: Anil Khanna (Ghaziabad), Kanwarjit Singh (Chief Commissioner of Income tax, retired), Sabornee Jana (Mumbai), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Vinod Mahajan (Delhi), Shishir Gupta (Indore), Ajay Ashok (Delhi), Shri Ram Aggarwal (Delhi)
Solved #Puzzle 174.1: Dr Vivek Jain (Baroda)
Solved #Puzzle 174.2: Dr Jeffrey Geist (Columbus, Ohio), Nitin Trasi (Sydney), YK Munjal (Delhi)
