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Problematics | Pet food for Diwali
There are just 20 kibbles to be shared among three kinds of pets. How many of them are dogs, how many cats, and how many mice?
A very happy Diwali to readers of Problematics, the fourth time we are celebrating the festival together since this column launched in its present form in Hindustan Times in 2022. We know from the previous three festivals that you will still take time out during your celebrations to solve my puzzles, so here are this week’s couple, carrying on a tradition that’s been unbroken for 165 weeks now.
#Puzzle 165.1
The pet store near my home is shut for Diwali and I realise too late that I have almost run out of TriPet Kibbles for my 20 pets, which include one or more dogs, a few cats, and a number of mice. I call up the store owner, who tells me he is out with his family but can only send me some kibbles in the evening, making a special case for my pets. In the meantime, I have to make do with whatever I have remaining.
The good thing about TriPet Kibbles is that they are safe for all three kinds of pets, with each kibble packing a significant amount of nutritional energy. The bad news is that I have only 20 kibbles left, and I need to distribute them in accordance with the nutritional needs of the three species. In the end, I decide that each dog will need 3 kibbles, each cat 1.5 kibbles and each mouse half a kibble; this will keep them active and playful until the evening. I then divide the 20 kibbles among my 20 pets, managing the exact required proportion. This required careful splitting pf some kibbles in half, but I managed that too by estimation.
The original version of this puzzle appears in the Bakhshali manuscript, an old Indian treatise dating between the 8th and 11th centuries. There were no TriPet Kibbles in those days, of course — and nor are there any now: that part is entirely my invention. But you will have guessed which way the puzzle is headed.
How many dogs, cats and mice do I have?
#Puzzle 165.2
This is a relatively easy puzzle that should not take up too much of your time during the festival. If you have seen the 1975 classic Jaws, you will likely remember the iconic sequence when the shark appears for the first time before police chief Brody (”You’re gonna need a bigger boat”). The monster is then seen by his two mates, with scientist Hooper assuming it’s 20 ft long long and shark hunter Quint estimating it’s likelier 25 ft.
The police chief is not heard giving his estimate in the sequence, so I asked him recently. “Well, I only saw the head at first,” he told me (and how well viewers will remember that enormous head popping out of the sea). “I guess the head was about 3 feet of the body out of the water,” Brody told me.
The rest of the dimensions are no longer available because Brody, as you remember, would ultimately blow up the shark. But by recent estimates given to me by Brody and Hooper (Quint, sadly, is no longer with us), the shark’s tail was equal to half its trunk plus its entire 3-ft head. Its trunk was half its entire length.
How long was the shark, the whole and the parts?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 164.1
Hi Kabir,
Suspect #1 has the disease of alternating between truth and falsehood; Suspect #2 always lies; Suspect #3 always tells the truth.
Suspect #1: Exactly two of the three suspects have the same disease. FALSE
Suspect #2: The murderer is not Suspect #3. FALSE
Suspect #3: The murderer is not Suspect #2. TRUE
Suspect #1: I am not the murderer. TRUE
Suspect #2: The murderer always lies. FALSE
Suspect #3: Neither of the innocents has the same disease as the murderer. TRUE
The murderer is Suspect #3
— Sabornee Jana, Mumbai
#Puzzle 164.2
Hi,
The total number of matches played among 5 teams is 10. Each match contributes 2 points (either 2 to the winner or 1-1 for a draw). So the total number of points is 10 x 2 = 20. The points from the mentioned matches add up 15. So Italy has 20 –15 = 5 points.
— Ajay Ashok, Delhi
Solved both puzzles: Sabornee Jana (Mumbai), Ajay Ashok (Delhi), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Vinod Mahajan (Delhi), Professor Anshul Kumar (Delhi)
Solved Puzzle 164.2: Anil Khanna (Ghaziabad), Shri Ram Aggarwal (Delhi)
(Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com.)
