Problematics | The truth about drinking
Two habitual liars and a truthful friend get drunk in a bar. Who drinks what?
Logic has sometimes been defined as mathematics without numbers, while some may argue that mathematics is actually logic with numbers. For puzzlers, it all boils down to the same thing: we are fine with whatever tests our reasoning skills, with or without numbers. Even word puzzles require reasoning.
People who habitually tell the truth or habitually lie provide us with puzzles that do not usually involve numbers, except for the number of such people involved in such a puzzle. One of the following puzzles brings a little variety to that category of puzzles. For more variety, the second puzzle involves both words and numbers.
#Puzzle 127.1
A bartender friend of mine, who knew I was looking for new puzzles, sent me a tip-off. Three people were visiting the bar, and one of them was known to always tell the truth while the other two always lied. For the moment, that was all the information that was available.
Keen to find out more, I made my way to the bar but reached rather late. I found my source clearing up empty bottles. “One of them has drunk several bottles of beer, another has downed a lot of whisky and the third is drunk on rum. In fact, all three are drunk,” the bartender told me.
We proceeded to their table, where I put my first question before the three men: “What have you just drunk?”
{{/usCountry}}We proceeded to their table, where I put my first question before the three men: “What have you just drunk?”
{{/usCountry}}Drinker #1: “I had rum.”
Drinker #2: “I did not have rum.”
Drinker #3: “I wasn’t the one who drank beer.”
I turned to the bartender: “In this drunken state, Is one of them still speaking the truth and the other two still lying?”
“Yes,” my friend confirmed.
From the information gathered so far, can we work what was drunk by any one of the three, or all three, or none?
#Puzzle 127.2
Take A =1, B = 2, C = 3… Z=26. In this puzzle, the “value” of any word may be defined as the product of the individual values of its letters, e.g. CANE = 3 x 1 x 14 x 5 = 210.
The crossword above is to be filled with 20 ordinary words, given the “values” of all those words:
Across: (1) 5016, (4) 55860, (6) 675, (7) 63000, (10) 1728, (11) 4370, (12) 13500, (15) 60, (16) 38000, (17) 72000
Down: (1) 133, (2) 120, (3) 1980, (4) 1330000, (5) 270864, (8) 6840, (9) 45125, (12) 900, (13) 54, (14) 625
To prevent any misunderstanding, the figures in brackets stand for cell numbers, and the “word values” are outside of the brackets.
Fill up the grid and mail it to me; you will probably find it easier than it looks.
MAILBOX: LAST WEEK’S PUZZLES
#Puzzle 126.1
Hi Kabir,
This puzzle made me nostalgic as my grandfather used to have this type of cubic calendar on his desk. The two cubes will have the following digits:
#Cube 1: 0, 1, 2, 6, 7, 8
#Cube 2: 0, 1, 2, 3, 4, 5
The face showing 6 can be used upside down to make 9.
I think condition #2 mentioned in the puzzle is not necessary to arrive at the solution. Both puzzles of this week seem to be the easiest so far, or I found the answers quickly.
— Anil Khanna, Ghaziabad
Hello Kabir,
Clearly, I have no idea what could be bothering you about this solution — or Gardner for that matter. The only thing I can think of is the 6 that is doubling up as 9. Many fonts may not allow this flip, but there are enough and more fonts available where such a switch is possible.
— Sanjay Gupta, Delhi
To make it clear, nothing was bothering Gardner. It was me; I had overlooked a crucial point in the puzzle, something that finally dawned on me much later than it should have. The original puzzle presented by Gardner was fine as it was. As Anil Khanna has pointed out, one of the conditions that I had introduced (because of my earlier doubts) was not necessary to arrive at the solution.
#Puzzle 126.2
Hi Kabir,
I started with manually solving this puzzle, but as multiple solutions started appearing, I thought it better to enumerate all the solutions using a program. The complete set of solutions is shown in tabular form.
— Professor Anshul Kumar, Delhi
Solved both puzzles: Anil Khanna (Ghaziabad), Sanjay Gupta (Delhi), Professor Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of Income-Tax, retired), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Aishwarya Rajarathinam (Coimbatore), YK Munjal (Delhi), Sabornee Jana (Mumbai), Shri Ram Aggarwal (Delhi), Ajay Ashok (Delhi)
Solved #Puzzle 126.1: Dr Vivek Jain (Baroda)
Solved #Puzzle 126.2: Shishir Gupta (Indore)