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Problematics | Birds in flight
Hedwig the owl and Kiki the parrot reach their owner at the same instant. Where is the boy standing?
Our main puzzle this week is an adaptation of an 11th-century Arabian original. Because readers have solved similar (if not identical) puzzles in these columns before, I have added some new details to my version. That said, it was interesting enough as it was in the original form. Neither version, however, is particularly difficult.
#Puzzle 206.1
A boy of 12, who loves Enid Blyton and Harry Potter, has named his pet parrot Kiki and his owl Hedwig. He lives in a one-storey house (ground floor with a terrace) on a street where the buildings are of variable heights. He lets his birds out every afternoon after returning from school, and calls them back in the evening when his mother reminds him it’s time for his homework.
One evening, when his mother has just called him in, the boy is on his terrace, which is 10 ft above the ground. He can see both his pets, one on a building to either side of him. The two buildings are 45 ft apart. Hedwig is to the boy’s left, on the terrace of a 4-storey building (40 ft from the ground). Kiki is to the boy’s right, on the water tank atop a 3-storey building (35 ft from the ground). The boy is 5 ft tall. Since the terrace is 10 ft above the ground, Hedwig and Kiki are 25 ft and 20 ft above him, respectively.
From a certain position on the terrace, the boy lets out a whistle. Hedwig and Kiki react at the same moment, each flying from its perch directly towards the boy. Both fly at the same speed. They reach the boy at the same time. Hedwig settles on the boy’s gloved hand while Kiki hops to his shoulder.
What is the boy’s horizontal distance from each of the two taller buildings?
#Puzzle 206.2
A motorist on a highway takes notice of a number shown on her odometer: 15951 km. “Ah, a palindromic number (reading the same both directions. A very rare sight indeed.”
Two hours later, to her surprise, she finds another palindromic number in km.
What is her driving speed? (From The Moscow Puzzles by Boris A Kordemsky)
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 205.1
Hello Kabir,
The order of the books from left to right is: (1) Moby Dick, (2) Heidi, (3) Animal Farm, (4) Wuthering Heights, (5) Great Expectations, (6) Emma, (7) Jane Eyre, (8) Frankenstein, (9) Pride and Prejudice, (10) Oliver Twist, (11) Dracula. The book chosen is Emma.
— Dr Sunita Gupta, New Delhi
#Puzzle 205.2
Dear Mr Kabir,
If the spectator declares that the product of the chosen number and 3 is even, the original number is twice the final answer revealed. If the product declared is an odd number, the original number is one more than twice the final result revealed.
Let the number chosen by the spectator be N. Multiplying by 3, the spectator gets 3N.
(i) If the spectator declares this product as an even number, the number is of the form 3(2K), where K is a natural number, N = 2K. The spectator divides it by 2 to get 3K, multiplies by 3 to get 9K, and finally divides by 9 to get K. This is the revealed final answer.
(ii) If the spectator declares the 3N product as an even number, the number is of the form 3(2K + 1), where K is a natural number, N = 2K + 1. The spectator adds 1 to get 3(2K + 1) + 1 = 6K + 4, divides it by 2 to get 3K + 2, multiplies by 3 to get 9K + 6, and finally divides by 9 to get K + 6/9. ignoring the remainder, the spectator reveals K as the final answer.
In both cases, the spectator announces K as the final answer. If the first product was announced as even, the chosen number is N = 2K. If the first product was announced as even, the chosen number is N = 2K + 1.
— Shri Ram Aggarwal, Palam, New Delhi
Solved both puzzles: Dr Sunita Gupta (Delhi), Shri Ram Aggarwal (Delhi), Yadvendra Somra (Sonipat), Professor Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Ajay Ashok (Delhi), Vinod Mahajan (Delhi)
Solved #Puzzle 205.1: Dr Vivek Jain (Baroda)
Solved #Puzzle 205.2: Shishir Gupta (Indore)
