Our favourite logic puzzles are those that can be done in your head, without pen and paper. We call them Hiking Puzzles because our friend Brian likes to pose and ponder them while hiking. Here are some of our favourites:
If you're interested in mechanical puzzles, then check-out Puzzle World, the best site on mechanical puzzles on the Internet!
1) Crossing the Bridge
Clem, Nancy, Toni, & Tim are going to a Canucks game at GM Place arena. They first have a pre-game dinner at Toni & Tim's place, and need to cross the Cambie Street Bridge to get to the concert. It is night and they only have 1 flashlight. There is the further problem that the bridge can only hold 2 people (this is where we stray from reality). Each of the band members have their own walking speeds but they need to share a flashlight so a pair must go as slow as the slowest one.
 | Clement takes 1 minute to cross the bridge. |
| Nancy takes 2 minutes to cross the bridge. |
| Toni takes 5 minutes to cross the bridge. |
| Tim takes 10 minutes to cross the bridge. |
The pre-game national anthems start in only 17 minutes ... do they make it on time for Tim to bellow out Oh Canada??
Assume that the time to get to and from the bridge to the stadium is negligible!
No stupid stuff allowed... everyone must cross completely with a light, one person doesn't start walking while the other is coming back with the light, no piggybacking, etc...
Solution to the Crossing the Bridge puzzle
2) 3 Light Switches
This is one of our all-time favourites:
On the ground floor of a house are three light switches, each with on/off labels. Upstairs in the same house are three light-bulbs in the ceiling of a single room. And yes, each switch downstairs controls a different one of the upstairs light-bulbs.
No tricks here - just three switches downstairs, three bulbs upstairs, and no indication as to which switch controls which bulb. Oh yeah, the bulbs upstairs are in a room with no windows - there is no way to see the bulbs without actually going upstairs.
Big Brian is downstairs and has had a really tough day skiing. He only has enough energy in him to climb the stairs once.
The question: How can Big Brian determine which switch controls which bulb? Remember - he can only go up the stairs once!
3) Monty's Revenge
Here it is - the classic! I'm told that a certain financial advisor in Edmonton is still working on this one.
Chris is a contestant in a game show called Monty's Revenge. In Monty's Revenge, there are three closed doors in front of Chris. Behind one of the doors is a fabulous prize (say tons of Kamei puzzles), behind the other two doors is something nasty (say Clem's hockey equipment).
Chris is asked to pick a door - which he does. Now, the host of the show, Monty, makes the following offer to Chris:
"Wait, wait, wait... Before you open that door and take what's behind it, let me make this a little more interesting. I know exactly where the fabulous prize is, so what I'm going to do is open one of the two doors that you didn't pick, where I know the prize isn't."
Monty opens one of the other two doors, and true to his promise, there lies some of Clem's hockey equipment.
Monty resumes his offer, "So, now we have two closed doors - the door you chose, and this other one here. Would you like to keep whatever's behind the door you chose - or would you like to change to this other closed door first?"
What should Chris do? Should he keep his door, or should he switch?
Just to make this interesting, we'll tell you the answer to the question above: Switch. Do it Chris! Switch!
Now for the real question: WHY??? (or if you don't believe us, prove us wrong)
This is not a trick question, nor a psychology question. It's straight-up probability (that's doable in your head with a little mental arithmetic.)
4) The Plate Game
Jana & Lori decide to play a game. They have a stack of plates which are all the same (Lori's fine china). They also have a round table (but the table could be square or rectangular).
Jana and Lori take turns placing a dish on the table-top, at any place which doesn't overlap with any other dish. The winner is the clever one who is the last person who is able to place a dish which doesn't fall off.
Lori, being the gallant guy that he is (oh yeah, Lori is a guy -- but that doesn't affect the problem), offers to let Jana to go first, if she wants to. What should Jana do to guarantee she wins??? (not that she's competitive)
5) The Puppy Puzzle
This one is a toughie. When Nancy called Clement this morning, his Golden Retriever was just having puppies. Clement told her that 2 male puppies had been born so far. Nancy was very excited.
Nancy rushed over to see the puppies, and found that there were 3 puppies in all! The puppies were playing -- two of them tumbled over each other and Nancy could see that they were both male (she blushed).
What are the chances that the other pup is also male?
6) Counterfeit Coins
Rob has ten piles of Canadian Loonies (a nifty $1 coin), numbered one to ten, plus a digital scale (not a balance). Each pile has 10 coins.
Rob knows that one whole pile of coins is counterfeit, with its coins each weighing one gram less than the correct loony weight. (Rob is a very astute guy, you see.) Oh yeah -- Rob knows what the correct loony weight is (he's good, eh?)
You guessed the question -- how can Rob find the bogus pile in a single weighing?
7) 6 Balls & a Scale
Eileen has 3 pairs of billiard balls, and a balance scale. The balance scale is one of those cheap models, and will break after two weighings.
One pair is black, one pair blue, and one pair red. In each pair, one of the balls is a little heavier than the other. All the heavy balls weigh the same. And all the light balls weigh the same.
Eileen has to identify all the light balls and all the heavy balls -- in But Eileen is a clever lass -- she finds a way... but there are no tricks here, just good old brute force logic! (a tough one to do in your head!)
8) 12 Balls & a Scale
Okidokee -- this may be the toughest puzzle on this page. Eileen decided to play with balls again (no reference to Andreas here). This is one of Brian's favourites - better wait for a long hike to try it... its a toughie and will likely take you a while.
Eileen still has her trusty old balance scale, and has 12 balls that appear identical. 11 of the balls have identical weight. The 12th ball is either slightly lighter or slightly heavier than the other 11 (we'll call this one the odd-ball). You don't know which ball is the odd-ball.
Fortunately, Eileen had her balance scale fixed. The repair guy told her that "it's better than before! This time it will break after 3 weighings."
So, in only 3 weighings, how can Eileen find the odd-ball, and determine if its lighter or heavier that the other balls. The method must be a "sure-thing" that works for Eileen every time.
This one also has no tricks, but it is tough!
