Problematics: Crop compensation, consolidated

A small community shares a field of 60 acres, half of it under paddy and half under wheat. After the losses, the community sends a young farmer to meet a middleman who claims he can get compensation processed on priority.

Middleman: For faster process, I’ll need to represent your paddy and wheat as a single crop with a unified compensation rate.

Young farmer: Explain.

Middleman: Let’s say a farmer has lost two acres paddy and three acres wheat. Under the current rates, he gets five tokens for his paddy and five for his wheat, which is 10 tokens for his five acres combined. Rather than claim separately for each crops, why not make a consolidated claim @ 10 tokens for five acres?

Farmer: Put that in context.

Middleman: You had 60 acres, both crops. At 10 tokens for every five acres consolidated, I’ll swing a deal for you at 120 tokens.

It’s only when the farmer returns home that the community notes something is wrong. Had they gone by the separate rate for paddy, or five tokens for two acres, then their first 30 acres would have given them 75 tokens. And at five tokens for three acres wheat, their other 30 acres would have given them another 50 tokens. That would have meant 75 + 50 = 125 tokens, not 120.  The middleman’s scheme was obviously to collect the full 125 tokens and give the farmers only 120.

Puzzle#8A: Root for the angry young man as he goes back to teach a lesson to the man who knew too much. But where did the five tokens disappear?

What you wrote

Puzzle #7A of last week attracted a number of new readers. Welcome to the cult.

So this is my jab at it. If Albert can’t guess what his label reads, it means that he must see either Boy/Girl or Girl/Girl.

Bernard can see Cheryl’s label. If Cheryl’s label reads Boy, he knows that his label can’t be Boy, else Albert would know that his own label reads Girl. Hence in this eventuality Bernard would know for certain that he is a Girl. Hence for Bernard to say he doesn’t know what his own label reads, Cheryl’s must read Girl. Phew.

Zahabia Rajkotwala (law student, Mumbai)

Right, Zahabia, and so are many others. Also, a new puzzle came up as a byproduct from this bunch of emails. In deducing Cheryl’s label as GIRL, have we also found out what labels Albert and Bernard are wearing? Various readers have various interpretations. I’ll go with Mansi, who narrows it down to two possible permutations.

Hello Kabir. My solution to Puzzle#7A. There can be 7 possibilities for Albert-Bernard-Cheryl.

1. G-B-B: Incorrect, since Albert would have guessed.

2. B-G-B: Incorrect, since Bernard would have guessed.

3. B-B-G: Incorrect, since Cheryl doesn’t know at first.

4. G-G-B: Incorrect, since Bernard knows that if he had BOY, Albert would have guessed.

5. G-B-G: Incorrect, since Cheryl knows that if she had BOY, Albert would have guessed.

6 & 7. G-G-G & B-G-G: In both these cases, Cheryl has GIRL and hence, definitely knows it.

I had fun solving this. Thank you.

Mansi Singh (New Delhi)

Mansi and I debated over the option G-B-G but she was right; it must be ruled out. That’s because if G-B-G was on, Cheryl would have guessed her label immediately after Albert had spoken. And we know she waited for Bernard to speak.

Meanwhile, here’s the answer to Puzzle#7B.

Open the box labelled C. As we know, all labels are wrong. The large box will have both red scarf and tie, or both blue scarf and tie. We could open just a single small box within C. If we find a red scarf, the other small box is bound to have a red tie. And so forth.

Case (i) Red scarf and tie: This would mean box B has contents of C and A has those of B.

Case (ii) Blue scarf and tie. This would imply that box A has contents of C and B has those of A.

Anirudha Hulsurkar (4th year civil, IIT Roorkee)

Roll of honour: Ayanansha Acharya, Biren Parmar (PhD student, Texas A&M University), Bindia George (IT engineer, Kochi), Sampath Kumar V (IIT Kozhikode alumnus) and Sanjay Gupta (New Delhi) have sent flawless answers to both Puzzles#7A and #7B.

Puzzle#7A only: Zahabia Rajkotwala and Mansi Singh, whose letters you have just read.

Puzzle#7B only:  Anirudha Hulsurkar.

Three others have reached Cheryl’s label after a few stumbles along the way. Harsha T R (NIT Karnataka, batch of 2012) insists G-G-G is the only possibility, while Sudarshan Shirsath (Kalyan, Maharashtra) and Melva Joseph rule out G-G-G altogether.

Three notes of music

The word CHAIRWOMAN may have gone out of fashion but it retains its charms. If you remove two of the 10 letters, for instance, you end up with CHAIRMAN without shuffling the letters. If you remove one letter, you get CHARWOMAN, again without rearranging.

Puzzle #8B (i): Remove one letter from CHAIRWOMAN and rearrange the remaining nine to get a musical instrument.

(ii) Remove the last letter from the musical instrument’s name but don’t rearrange. Your eight-letter word is still connected with music.

(iii) Go back to the musical instrument, remove two letters and rearrange the remaining seven to form another musical instrument.

Please send your replies to:

kabir.firaque@expressindia.com