Problematics | Superhero fact and fiction
Which one(s) among Superman, Batman and Robin tell(s) the truth, and which one(s) lie?
Although I bring you fresh puzzles week after week, not all of them are original creations of mine. Some are taken directly from other sources, and some I adapt. These adaptations can provide a great deal of satisfaction if embellished well enough.
Here, then, is one such puzzle. I came across the original recently, and I have used its core principle to create my own, but I have done so much work on it that I would call it less an adaptation than a semi-original puzzle. I hope you enjoy it.
#Puzzle 129.1
A strange virus with two strains is spreading across human populations. Those infected by the Fact Strain always speak the truth, even in tricky situations where lying might have been seen as a practical option. The Fiction Strain, on the other hand, turn infected people into uncontrollable liars.
All sorts of people, from heroes and ordinary folk to petty thugs and supervillains, are getting infected with one strain or the other. Superheroes too. Word reaches me that Superman, Batman and Robin are all afflicted, but the information is vague about which strain has infected whom. Sensing the possibility of a new puzzle, I ask a contact to get in touch with the superheroes and record the conversation. My contact interviews the three together, and mails me the audio file.
I shall not bore you with the full details of the conversation. After editing out the greetings and other small talk, only three statements (one each by Superman, Batman and Robin) seem to be of value:
Statement #1: Of the two heroes among us whose names include a R, one always lies and the other always tells the truth.
Statement #2: The two heroes among us whose names include an B are either both liars or both truthful.
Statement #3: Of the two statements just made by my colleagues, at least one is factual, i.e. they may/may not include one lie, but not both can be lies.
Since the speakers in the voice recordings have not identified themselves by name, I call my contact: “Which one made which statement?”
“I don’t remember who said what,” my contact says apologetically, “but I do remember that each superhero made one statement. I also noticed something else that may be helpful.”
“What?” I am disappointed, and not really hopeful that what he has noticed will be of any use.
“It’s about the letters R and B, which may be important,” he says.
“Of course they are,” I reprimand him. “These two letters are key to the solution.”
“While making notes, I may have missed who said what, but I did write down something interesting,” he says.
“You already mentioned that,” I say, getting impatient.
“Well, both heroes with an R in their names gave statements that include one or more Rs. And both heroes with a B in their names gave statements that include one or more Bs,” my contact tells me.
Hopes rising, I quickly run a program and convert the audio file into text.
“Thank you,” I tell my contact, while examining the ₹and the Bs in the three text sentences. “I now know…”
… Who said what, and who is infected by which strain of the virus?
#Puzzle 129.2
In an age before mobile phones and computers became household items, the typewriter used to be a fascinating device. For the benefit of younger keyboarders of the internet generation who might never have used a typewriter, let us state what oldies know well: the alphabetical characters on a computer or mobile keyboard are in the same arrangement as in a typewriter. The top row is QWERTYUIOP, followed by ASDFGHJKL, and finally ZXCVBNM.
Using only the letters of the top row, any of them any number of times, but no letter from the second and third rows, what is the longest dictionary word you can type out?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 128.1
Hello Kabir,
The answer is in tabular form, as required.
Problematics has, kind of, become a part of the Monday morning ritual. One does tend to wait for the online version to pop up. In fact most often, I skip the puzzles of the day and go right down to the answers of last week to check how one has fared. Only then do I 'page-up' to read the new puzzles. Kindly keep up the good work.
— Sanjay Gupta, Delhi
Dear Kabir,
Let the number with five digits be abcde. Its value is (10000a+1000b+100c+10d+e). If we subtract a + b + c + d + e) from it, we get (9999a + 999b + 99c + 9d), which is 9(1111a + 111b + 11c + d). This is a multiple of 9, therefore the sum of its digits will be a multiple of 9. In case we remove any one digit, the sum of the remaining digits will fall short of 9 by the value of the digit removed. So if the person playing the trick is told the sum of the remaining digits, they will know that the deleted digit must be (9 – x), where x is the sum of the remaining digits.
The only exception is when the sum of the remaining digits comes to 9 (or a multiple of 9 for larger numbers). In other words, this problem will arise when the digit removed is either 0 or 9. For this another question will help find out whether the digit removed is 0 or 9. The person playing the trick may ask, for example, “Is the number omitted more than 4?” Then it can be determined whether 0 or 9 was removed.
— Yadvendra Somra, Sonipat
As Yadvendra Somra and a couple of other readers have pointed out, there will be an exception when the sum of the unremoved digits is 9 or a multiple. This was an omission on my part. After readers pointed this out, I thought about revising the puzzle by adding a condition that the removed digit cannot be 0, but then decided against it since the puzzle had already been live for some time. Yadvendra Somra’s suggestion about an additional question looks like a nice embellishment to the puzzle.
Among other omissions was the name of Amarpreet. He had correctly solved both Puzzles #127.1 and #127.2 correctly, but then I mistakenly left his name out while compiling the list of solvers last week.
Solved both puzzles: Sanjay Gupta (Delhi), Yadvendra Somra (Sonipat), Dr Sunita Gupta (Delhi)
Sabornee Jana (Mumbai), Shishir Gupta (Indore), Aishwarya Rajarathinam (Coimbatore), Professor Anshul Kumar (Delhi), Ajay Ashok (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired)
Solved #Puzzle 128.1: Amarpreet (Delhi)
Solved #Puzzle 128.2: Biren Parmar (Bay Area, California), Vinod Mahajan (Delhi), YK Munjal (Delhi)