Image by Flickr user "sparktography" - used via Creative Commons license.

Congrats to Jeff L. who nets himself a $50 gift certificate from ThinkGeek! Keep reading for his unexpected solution.

Puzzle

Super spy extraordinaire Pedro Vex is in deep trouble. During what was supposed to be a covert operation, he’s just walked into a room full of underpaid henchmen ready to take him down. It’s a set-up! Pedro stands in the doorway and prepares to fight. He quickly takes a mental inventory of the position of the henchmen, their weapons and any visual weaknesses. He also wonders how a spy of his caliber can fall into such a trap. He only has seconds before battle, these are his split second observations. Can you determine the position of each idiot in the room, their weakness and their weapon?

The sleeping henchman is not standing by the file cabinet and he’s not holding a katana.
The henchman sitting at the desk isn’t holding a machine pistol.
The henchman who is clearly drunk isn’t standing at all. And he has a battle axe.
The henchman in front of the window isn’t as cross eyed as the guy standing in the middle of the room.
The flipper armed henchman is not holding a mace or standing next to the file cabinet.
The henchman with the katana is standing by the radiator.
The short henchman is not holding a 2×4, neither is the cross-eyed henchman.

Solution

While the solution can be presented in a basic logic chart (there were enough clues and other points of logic to build the table with the use of keen powers of deduction) Jeff had a completely different, though logically correct solution, which is presented in full below the chart. He also was kind enough to include his own completely geeky illustration of the puzzle solution.

Solution Logic Grid

Jeff’s solution

Okay, quite simply, this puzzle deals with concrete facts and assumptions that are irrelevant. Simply because someone is NOT holding a mace, for example, doesn’t mean a mace IS being held by anyone. It could be a herring, or a dolphin, or any other equally-proficient bludgeoning instrument; all we know is that it is not being held… possibly not present at all! Whoa.

Without further ado, below please find the aesthetically-pleasing graphic illustration that melds all known factors from the eyes of Pedro Vex into one cohesive, accurate solution of the puzzle at hand (explanation follows illustration):

The questions requiring answers and those answers in short, are:

1. Can you determine the position of each idiot in the room? YES.
2. Can you determine said idiot(s)’s weakness? YES, given a degree of assumption.
3. Can you determine their weapon? Of the henchmen, YES, but not that of Pedro Vex.

1. The position of each idiot. There are two possibilities, or, everyone is an “idiot”:

a) From the eyes of Pedro Vex, we ASSUME the “idiots” are the two henchmen, although the intellect of the henchmen were never given, suffice to say being drunk and asleep isn’t the best method for ambushing and taking-out a super spy extraordinaire. ASSUMING the idiots are the henchmen, one is asleep in front of the window at the desk under a window, drunk, and the other is standing in the middle of the room by a radiator.

b) From the eyes of the henchmen, clearly the “idiot” is Pedro Vex as he has fallen into such a trap - sprung by a drunkard and a cross-eyed evil-doer, nonetheless. The only conceit is that Pedro is either “standing in a doorway” or “he’s just walked into a room,” which appears to be a logical fallacy. However, for the sake of argument and a potential unreliable narrator we’ll say Pedro has “just walked into (the) room” allowing him to be a potential idiot as he is in the room.

2. Determining the idiot(s)’s weakness. (Following the same rubric established in question one:)

a) From the eyes of Pedro Vex, the chief weakness of the henchman in the center of the room, Jimmay, we’ll call him, is that he is cross-eyed. Timmay, of course, is both drunk and asleep at the desk, thus he is presently combat ineffective. Intellectually, they are idiots since they are but mere underpaid henchmen - opposed to crime bosses or crime lords or something equally savvy.

b) From the eyes of the henchmen, the chief weakness of Pedro Vex is both his ineptitude for falling into traps and wearing a ridiculous costume which would constrict movement, to say nothing of not allowing him to maintain an espionage persona, unless his cover is a Dragon Con attendee.

3. Determine their weapon.

a) Jimmay is holding a katana. Timmay has a battle axe.

b) Pedro: we are not given sufficient information to determine if he is armed.

The meat of the matter.

To substantiate the illustration above, artistic license notwithstanding, we deduce what we know from we do NOT know. Again, simply because someone is not standing by a file cabinet does not mean that someone is standing by a file cabinet. Hell, we can only assume a file cabinet is present at all. This is just fluff, trying to throw us critical thinkers off the scent. For grins, we’ll keep the cabinet but only because the pet headcrab likes to hang-out up there. Take away message: cull the fluff from the substance. What we know for certain is that there are AT LEAST TWO HENCHMEN that are armed at two separate parts of the room. All else is unsubstantiated speculation.

Jimmay, the cross-eyed henchman is standing in the center of the room next to a radiator, holding a katana. His position, disposition, description, etc., are all substantiated by the following numbered bullets (reference below): #1 (he isn’t asleep), #4 (he is cross eyed guy standing in the middle of the room and he is not the henchman in front of a window), #5 (either has a flipper for an arm or is armed with a flipper… unclear, possible… but again, not concrete and allows for a flipper and katana weapon as both can be operated with one arm each, perhaps), #6 (the henchman with the katana standing by the radiator)

Timmay is the drunkard in the chair, fast asleep at the desk which is positioned underneath a window. This claim is substantiated by the following numbered bullets: #1 (sleeping), #1 (not standing), #1 (not holding a katana), #2 (sitting at the desk), #2 (not holding a machine pistol), #3 (clearly drunk, not standing at all, has battle axe), #4 (in front of window, not as cross eyed as guy in middle of room, so there is a guy in the middle of the room), #5 (either has a flipper for an arm or is armed with a flipper… unclear, possible… but again, not concrete and allows for a flipper and battle axe weapon as both can be operated with one arm each, depending on model of the axe… and flipper), #7 (not holding a 2×4… but also isn’t holding the grand canyon or a lightsaber; worthless information aside from the fact that he isn’t the cross-eyed henchman, of course)

Given information:
1. The sleeping henchman is not standing by the file cabinet and he’s not holding a katana
2. The henchman sitting at the desk isn’t holding a machine pistol
3. The henchman who is clearly drunk isn’t standing at all. And he has a battle axe.
4. The henchman in front of the window isn’t as cross eyed as the guy standing in the middle of the room.
5. The flipper armed henchman is not holding a mace or standing next to the file cabinet.
6. The henchman with the katana is standing by the radiator.
7. The short henchman is not holding a 2×4, neither is the cross-eyed henchman.

In sum, the logic fits the puzzle and is not speculative. There are only two henchmen for certain in the room.

Stay tuned next week for another fun puzzle!

Image by Flickr user "sparktography" - used via Creative Commons license.

Super spy extraordinaire Pedro Vex is in deep trouble. During what was supposed to be a covert operation, he’s just walked into a room full of underpaid henchmen ready to take him down. It’s a set-up! Pedro stands in the doorway and prepares to fight. He quickly takes a mental inventory of the position of the henchmen, their weapons and any visual weaknesses. He also wonders how a spy of his caliber can fall into such a trap. He only has seconds before battle, these are his split second observations. Can you determine the position of each idiot in the room, their weakness and their weapon? Email your solution by Friday at 10:00 pm EST to be part of the selection from correct answers to win a $50 gift certificate from ThinkGeek!

The sleeping henchman is not standing by the file cabinet and he’s not holding a katana.
The henchman sitting at the desk isn’t holding a machine pistol.
The henchman who is clearly drunk isn’t standing at all. And he has a battle axe.
The henchman in front of the window isn’t as cross eyed as the guy standing in the middle of the room.
The flipper armed henchman is not holding a mace or standing next to the file cabinet.
The henchman with the katana is standing by the radiator.
The short henchman is not holding a 2×4, neither is the cross-eyed henchman.

Photo: MonkeySimon/Flickr (CC)

Last week we had you work your logic muscles to solve the conundrum of who ate the most fudge during a friendly game of D&D. Congratulations to Scott for having his correct answer randomly chosen. He’ll receive a $50 gift certificate from ThinkGeek!

Puzzle

This week, we have a group of geeks playing D&D and eating fudge. We need to know who ate how much. E-mail your answer to us by Thursday 10 PM EST for your chance to win a $50 gift certificate to ThinkGeek!

Four geeks and super-logicians were playing their regular D&D Saturday night game at the Logician’s Club headquarters (where they’re all members). One of them had brought the left-overs of a batch of fudge they had made earlier that day. There were 11 pieces, all exactly the same size. The game, as always, was intense, and they ended up eating all of the fudge. Each geek knew how much fudge they had consumed. Nobody knew how much any of the others had eaten, except that each person had eaten at least one piece. At the end of the evening, they wanted to know who had eaten how much, so they agreed to ask only questions to which they didn’t know the answers. Here are the questions:

Albert: Did you eat more pieces of fudge than I did, Betty?
Betty: I don’t know. Did you, Stephanie, eat more fudge than I?
Stephanie: I’m not sure.
Kurt: Aha!

Kurt figured out how many pieces of fudge each geek had eaten. Can you do the same?

Solution

Answer:
Kurt: 5 pieces
Stephanie: 3 pieces
Betty: 2 pieces
Albert: 1 piece

Reason:
The inability to answer the question “Did you eat more than me?” can be used to determine “at least so many pieces” for each person. Everyone knows that everyone else had at least one piece. When Albert asked Better if she had more than him, she is unsure. If she only had one piece, the answer would have been absolute (”No, I didn’t”). Consuming only one piece would be at best the same number as him. Her uncertainty indicates she had at least two pieces and not sure if Albert only had one.

Betty then asks the same question to Stephanie. Stephanie is also unsure; however she has heard the previous question & answer. Therefore, Stephanie had more than one piece (same logic as before), PLUS she had more than two pieces. If Stephanie only had two pieces, then her answer to the question would have been “No, I didn’t have more than you.” Stephanie must have had 3 or more pieces.

Kurt, upon hearing these questions / answers is able to solve the problem. Therefore, this information & reasoning must provide him with enough information. Since he knows how much he’s consumed, that Albert had at least one, Betty had at least two, and that Stephanie had at least three, Kurt must have had five pieces to solve the problem at that moment. If only four pieces, he could not have know the solution and consuming six is not possible with only eleven total

With Kurt eating 5 pieces, the rest falls out because of 11 pieces to start with, Stephanie had only 3, Betty had 2, and Albert only 1 piece.

Thanks for playing! Visit ThinkGeek! and enter GEEKPUZZLER for your $10 discount on a $40 or more purchase.

Photo: MonkeySimon/Flickr (CC)

This week, we have a group of geeks playing D&D and eating fudge. We need to know who ate how much. E-mail your answer to us by Thursday 10 PM EST for your chance to win a $50 gift certificate to ThinkGeek!

Four geeks and super-logicians were playing their regular D&D Saturday night game at the Logician’s Club headquarters (where they’re all members). One of them had brought the left-overs of a batch of fudge they had made earlier that day. There were 11 pieces, all exactly the same size. The game, as always, was intense, and they ended up eating all of the fudge. Each geek knew how much fudge they had consumed. Nobody knew how much any of the others had eaten, except that each person had eaten at least one piece. At the end of the evening, they wanted to know who had eaten how much, so they agreed to ask only questions to which they didn’t know the answers. Here are the questions:

Albert: Did you eat more pieces of fudge than I did, Betty?
Betty: I don’t know. Did you, Stephanie, eat more fudge than I?
Stephanie: I’m not sure.
Kurt: Aha!

Kurt figured out how many pieces of fudge each geek had eaten. Can you do the same?

Warning: Causes Visions

Robin B. correctly identified the age at which Bob Frank saw himself live in his turkey induced vision and nets a $50 gift certificate from ThinkGeek!

Puzzle

The Frank family just finished up their Thanksgiving dinner. Bob Frank, the youngest cousin, capped off his dinner with half of a pumpkin pie. This was after four servings of Turkey, a ton of ham, sweet potatoes, corn, three rolls and stuffing. He’s already got the meat sweats, and now with the addition of all the sugar from the pie - Bob has gone into a walking food coma. Suddenly he becomes quite confused as to where he is and who all the people around him are. Bob looks around and the world is spinning. Suddenly he sees his whole life and death flash before his eyes - even the age at which he will die. He sees his youth lasted 1/6 of his life. In the next 1/12 of his life he had his first beard. At the end of the following 1/7 of his life, he got married. Five years later his daughter was born. His daughter lives exactly 1/2 of Bob’s life. Bob dies 4 years after the death of his daughter. How long did Bob live in his vision?

Solution

Diophantus was a Greek mathematician from Alexandria, commonly referred to as the father of algebra. He lived around 3rd century A.D. The point of that? Well, his life was described by an admirer of his by this algebraic riddle, which is what the puzzle above was based on.

1/6x + 1/12x + 1/7x + 5 + 1/2x + 4 = x
x=84

Or, Robin’s solution:

Proof derivation:
Let X = Bob’s age
Let Y = Bob’s daughters age

X = 2Y
X = (1/6)X + (1/12)X + (1/7)X + 5 + Y + 4

Merge two equations together and then solve for Y:
2Y = (1/6)X + (1/12)X + (1/7)X + Y + 9
Y = (1/6)X + (1/12)X + (1/7)X + 9
Y = (11/28)X + 9

Plug original X = 2Y equation into resultant equation above:
Y = (11/28)(2)Y + 9
Y = (22/28)Y + 9
Y = 42

X = 2Y = (2)(42) = 84

Thanks for playing and stay tuned for another puzzle on Monday!

Know Your Limits, Avoid the Turkey Hangover.

The Frank family just finished up their Thanksgiving dinner. Bob Frank, the youngest cousin, capped off his dinner with half of a pumpkin pie. This was after four servings of Turkey, a ton of ham, sweet potatoes, corn, three rolls and stuffing. He’s already got the meat sweats, and now with the addition of all the sugar from the pie - Bob has gone into a walking food coma. Suddenly he becomes quite confused as to where he is and who all the people around him are. Bob looks around and the world is spinning. Suddenly he sees his whole life and death flash before his eyes - even the age at which he will die. He sees his youth lasted 1/6 of his life. In the next 1/12 of his life he had his first beard. At the end of the following 1/7 of his life, he got married. Five years later his daughter was born. His daughter lives exactly 1/2 of Bob’s life. Bob dies 4 years after the death of his daughter. How long did Bob live in his vision?

E-mail your answer by 10:00 PM EST Friday (note the extra day!) to have it included in the drawing for a $50 gift certificate from ThinkGeek!

*All Characters are fictional. Any similarities to your family or someone you know are entirely coincidental.

Photo: Flickr/laurgasms (CC)

I gave you all an easy puzzle for Thanksgiving and you responded well. We received over 250 responses! Congratulations to Dan for having his answer randomly chosen from among all the correct answers! He’ll receive a $50 gift certificate from ThinkGeek! Puzzle and solution follow.

Puzzle

While we were preparing the menu for our upcoming feast, my wife asked how many guests we’ll be having. Being the geek that I am, I answered: Half are from out-of-state, one quarter are from in-state but out-of-town, one seventh are from across town, and those who live in this house are the remaining three.

How many guests are we having? Why do I have to eat outside?

Dan’s Solution

How many guests are we having?
Total: 28
Out-of-state: 14s
1/4 in-state but out-of-town: 7
1/7 across town: 4
Your house: 3

Why do you have to eat outside?
Your wife was none too happy about getting the run around instead of a solid number.