Problematics | The rate of gunfire
A gunmaker claims he can fire his weapon at a certain rate. Has he delivered what he promised?
In his column Mindsport, which he ran for 10 years in The Illustrated Weekly of India, the late Mukul Sharma invariably presented one challenging puzzle followed by a simpler one. More accurately, the puzzle presented first was intended to be tougher than the second one, but then tough and easy are relative terms.
This is something I have come to accept in the course of frequent interactions with Problematics readers. Last week’s puzzle about cricket siblings, for instance, was intended to be the tougher one but everyone who attempted it got it correct. The puzzle about seating of couples, on the other hand, was intended to be the simpler one but quite a few readers got it wrong.
During the years when I was regularly following Mindsport, there would occasionally be a puzzle that came across to me as relatively simple but was presented it as the week’s main fare. Among them, I had been ignoring the following one over the years I have been writing Problematics. Then I came across the same puzzle among Henry Ernest Dudeney’s writings. If two greats can set the puzzle, there must be something in it. So, here goes.
Puzzle #131.1
A government committee, looking for automatic weapons that fire rapidly, invites applications from private firearm manufacturers. Applications arrive, and the committee tests the products and places orders for various weapons with various firing speeds. It does not bother the committee so much that some firearms are less rapid than others (not everything can be equal) as long as each weapon has other advantages. What the committee is fussy about, however, is that the manufacturer should not bluff about the specifications: they had better deliver what they promised, otherwise no deal.
One gunmaker, an individual without a company, offers an automatic which, he claims, can discharge its ammunition @1 round/second. Prove it, the committee says, and takes him to the shooting range. Fire, they instruct the gunmaker, and start a stopwatch, which they stop after exactly one minute.
How many shots, the committee supervisors ask the fellow who was counting.
“Sixty rounds in 1 minute,” says the counting man.
“I told you so,” says the gunmaker, a delighted smile lighting up his face. “Deal?”
“No deal,” says the committee, shaking their heads in exasperation.
Deal or no deal?
Puzzle #131.2
Two parents are teaching their daughter arithmetic. They unpack a box of marbles and ask the child to take out as many as she likes. Using both hands, she takes them out in batches until she has collected what she thinks is a largish pile.
The parents now distribute the remaining marbles between themselves, unequally, and ask the child to count each of the three sets. She does, and observes that her pile isn’t as big as she thought. “The marbles in my pile are only 1/5 of the total.”
“Here, take mine,” her father says, handing over his entire pile. The delighted child merges the two piles and recalculates: “I now have 3 times as many as Mother.”
“Let’s redistribute them,” her father says, and takes 200 marbles back from her.
His wife now asks their child to calculate: “How much more do we have than you?”
“Together,” the child works out in a flash, “the two of you have twice as many as I.”
Who had how many marbles at the first distribution?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 130.1
Hi Kabir,
Let us assume that each player played a number of matches equal to their initial. So, Arjun played A matches, Bharat played B… and Kamala played K matches. Given,
A – E = 3; G – H = 2; B² – C² = 76; D² – H² = 48
Solving the third and four equations for integer values (and for B, C and D to be even), we get
B = 20; C = 18; D = 8; H = 4. Now from the second equation we get G = 6.
This means any one of A, B, C, D has to be 2G or 12. Since we already have the values of B, C, D, only A can be 12. Now from the first equation we get E =9. This gives us all the sibling pairs and the value of K = 10 (see table).
This puzzle was quite interesting, requiring a combination of mathematical calculations and a little logic.
— Anil Khanna, Ghaziabad
#Puzzle 130.2
Hello Kabir,
I have tried to solve this without writing too many details. Sending an image based on the given conditions [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]. In any combination, Mr Chatterjee has to be the sound recordist.
— Dr Sunita Gupta, Delhi
Dr Gupta’s original solution has diagrammatical representations for Case #1 and Case #2. Both of these seat Mr Das on the right edge (from his perspective) of his side of the table. I have added Case # 3 and Case #4, which are the same as Case #1 and Case #2 respectively, except in one respect: Mr Das is now seated on the left side (again from his perspective) of his side of the table.
In any case, only Mr Chatterjee’s profession can be asserted with certainty: he is the sound recordist. A few readers have given both professions with certainty. These must be counted as wrong because, as the illustration shows, the graffiti artist’s name cannot be established for certain.
Solved both puzzles: Anil Khanna (Ghaziabad), Dr Sunita Gupta (Delhi), Sabornee Jana (Mumbai), Aishwarya Rajarathinam (Coimbatore), Yadvendra Somra (Sonipat), Professor Anshul Kumar (Delhi), Abhinav Mital
Solved Puzzle #130.1: Shishir Gupta (Indore), YK Munjal (Delhi), Ajay Ashok (Delhi), Vinod Mahajan (Delhi), Shri Ram Aggarwal (Delhi), Sanjay Gupta (Delhi)
Sanjay Gupta has also pointed out errors in a couple of the answers to Puzzle #129.2: “Your readers have given four answers of 11 letters each. Two of them are wrong. TYPEWRITTEN uses N, which is on the last row of the keyboard, and PROPRIETARY uses A, which is on the middle row. Hence both these words should technically be disqualified.”