Wednesday, May 6, 2009
Find a positive integer whose first digit is 1 (1abcde...) and when the 1 is moved to the opposite side (abcde...1) the number has tripled.
Cubes - Math Puzzle
Consider any 3 consecutive integers. Prove that the sum of the largest can not equal the sum of the cubes of the other 2.
Polynomial - Math Puzzzle
Suppose that f(x) is a polynomial with non-negative integer coefficients.
How would you be able to determine the polynomial in under 10 questions in which the form of the question you can ask is f(k) = ? Where K = any integer value you request.
2=1 Math Puzzle
Proof that 2=1:
a = b
a^2 = ab
a^2 - b^2 = ab-b^2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1
Why is this argument false?
Solution (Highlight): In step 5 you can not divide by zero.
Where's the father? - Math Puzzle
The mother is 21 years older than the child. In 6 years from now, the mother will be 5 times as old as the child. Question: Where's the father?
Solution (Highlight):
m=d+21
m+6=5(d+6) > m=5d+24
Substitute and find that d=-3/4 or -9 Months.
The father is on top of the mother.
Unusual Paragraph
How quickly can you find out what is so unusual about this paragraph? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you look at it, study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour. So jump to it and try your skill at figuring it out. Good luck --don't blow your cool.
Solution (Highlight): I think you should wait a day or two for this. O and this solution also has that unusual quality too
Half Full or Half Empty? - Logic Puzzle
You are in an empty room and you have a transparent glass of water. The glass is a right cylinder, and it looks like it's half full, but you're not sure. How can you accurately figure out whether the glass is half full, more than half full, or less than half full? You have no rulers or writing utensils.
Solution (Highlight): Tilt the glass to the side so that the water reaches the open end of the cup, but none spills out. If the water on the inside of the cup covers exactly the base of the cup, it is half full. Any more and it is more than half full and any less and it is less than half full.
Poisoned Wine
Tuesday, May 5, 2009
You are an evil king with 1000 bottles of wine. One day one bottle of wine is poisoned. You are unsure of exactly which bottle of wine is poisoned, but have 10 prisoners in the dungeon upon which to test.
The poison takes 1 month to kill, and it shows no side effects. You need all of the wine for a party happening in 5 weeks, what do you do?
Solution (Highlight): Arrange the wine in a 10x10x10 cube.
On the first day:
Prisoner 1 will sip wine from the top 10x10x1 square.
Prisoner 2 will sip from the 2nd 10x10x1 square.
...etc...
Day 2:
Prisoner 1 will drink from the first 10x1x10 square.
Prisoner 2 will drink from the 2nd 10x1x10 square.
...etc..
Day 3:
Prisoner 1 will drink from the first 1x10x10 square.
Prisoner 2 will drink from the 2nd 1x10x10 square.
...etc...
After one months time one prisoner will die, that will indicate which 10x10x1 square had poison.
After another day passes one more prisoner will die. That will indicate which 10x1x10 square held poison.
After one more die a final prisoner will die giving us the final 1x10x10 square.
The intersection of these squares will be the poisoned bottle.
It's a long Solution.
Cigars - Puzzle
Because cigars cannot be entirely smoked, a Hobo who collects cigar butts can make a cigar to smoke out of every 5 butts that he finds. Today, he has collected 50 cigar butts. How many cigars will he be able to smoke?
Solution (Highlight): He will be able to smoke 12 cigars. 50 butts = 10 cigars = 10 butts = 2 cigars. 10+2=12
5 Digit Number - Logic Puzzle
A five digit number exists such that:
- The first digit is a prime number.
- The second digit is the fifth digit minus the first digit.
- The third digit is twice the first digit.
- The fourth digit is the third digit plus three.
- The fifth digit is the difference between the first digit and the fourth digit.
Also no digit equals zero and no digit is repeated. What is the 5 digit number?
Solution (Highlight): 23475
Consecutive Integers - Math Puzzle
In the equation shown below, A, B, C, D, and E are 5 consecutive positive integers. What are they?
A*A + B*B + C*C = D*D +E*E
Hourglasses - Logic Puzzle
You have two hourglasses. One times 7 minutes, the other 11. Using just these hourglasses, accurately time 15 minutes.
Solution (Highlight): Flip both the 11 and 7 minute hourglasses over. Once the 7 minute runs out turn it back over. Once the 11 minute hourglass will finishes turn the 7 minute over one more time(4 minutes worth of sand are in the bottom). 11+4 = 15
Desert Crossing - Math Puzzle
A traveler wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?
Note all men must survive.
Gold Chain - Logic Puzzle
A man needed to pay his rent and was out of money, but found that his rent was worth about one gold link on his chain per day. What is the fewest number of cuts he can make in his 23-link chain to pay the rent daily for up to 23 days?
After making the cuts he will be able to pay the landlord each day. i.e. He will pay the landlord on the first day, the second day, the third day........and the 23rd day. Therefore he cannot just give him the whole chain.
A Doctor, A Lawyer, A Teacher - Logic Puzzle
Jason, John and Joe are a doctor, a lawyer, and a teacher. The teacher, who is an only child, earns the least money. Joe, who married Jason's sister, earns more than the lawyer. What is each man's job?
Marbles - Logic Puzzle
You have fifty bags, each with approximately one hundred balls inside.You have a weighing machine with a digital readout, with 3 places of decimals on the display, calibrated in grams, it is capable of weighing an infinite amount (but it won't have to).
All of the balls in all of the bags weigh 1.000 gram, except in one bag in which all of the balls weigh 1.001 grams.
You cannot tell by look or feel which bag has the heavier balls.
How do you determine which bag contains the heavier balls?
Note: The weighing machine may only be used once.
Word Puzzles
You may have to think outside of the box for these.
You are trapped in a room with 10 foot thick steel walls, no door, no window, nothing. You have a piece of wood and a saw. How do you get out?
You are trapped in the same room with only a baseball and a bat. How do you get out?
You are again trapped in the same room with only a piano, this time however, a locked door is added to the room, how do you get out?
As a side note I am currently working on getting a base of puzzles before I will focus on putting solutions up. The base of puzzles and solutions should be extensive by the end of the month, so be sure to check back.
The Tiger, The Goat and some Cabbage - Logic Puzzle
A man is traveling with a tiger, a goat, and a cabbage.
The man came to a river which was too deep to wade across, and too wide to swim across so he was in a quandary on how to continue. He noticed a small boat tied to the near shore, but the boat was too small to hold all his belongings, but was large enough that he could safely row across with one belonging at a time.
The problem he faced was that if he rowed across with the tiger then the goat would eat the cabbage, and if he rowed across with the cabbage, the tiger would eat the goat.
How could the man cross the river safely with all his belongings intact?
Four 7's = 56 - Math Puzzle
Manipulate four 7's using addition, subtraction, multiplication and division to reach 56.
Solution (Highlight): ((7/7)+7)*7 = (1+7) *7 = 8*7
Pencils - Logic Puzzle
You must arrange 6 pencils in such a way that any 2 are touching. Or that each pencil touches each of the other 5 pencils.
How must the pencils be arranged?
Solution (Highlight):
Place the pencils in sets of 3 side by side:
|| || ||
Next make a triangle out of the 3 groups of pencils.
Strings - Logic/Math Puzzle
You have two strings that when you light one end of either string it takes exactly one hour to burn.
The rate at which the strings will burn is completely random and each string is different.
How do you measure 45 minutes?
Solution (Highlight): Light both ends of one string and one end of the other string. After the first string has burnt out 30 minutes will have passed and the first string will be 30 minutes through it's burn time as well(Not necessarily half way through though). Immediately light the other end of the second string. It will take 15 minutes for that string to burn out, resulting in 45 minutes elapsed time.
Water Bucket - Math Puzzle
You have a three gallon and a five gallon bucket. You wish to measure out exactly four gallons.
How do you do this?
Solution (Highlight): Fill the 5 gallon bucket and empty it into the 3 gallon bucket. Empty the 3 gallon bucket and move the water(2 gallons) from the 5 gallon bucket into the 3 gallon bucket. Fill the 5 gallon bucket and pour one gallon into the 3 gallon bucket.
Desert Race - Logic Puzzle
In his final will a prince of the desert says that he will give all of his riches to one of his two sons.
They will have a competition, they must race their camels through the desert. Whichever son's camel crosses the finish line last will win.
After wandering aimlessly around the desert for days both sons come across a wise man.
After hearing the wise man's words both sons race to the finish line.
What did the wise man tell them?
Solution (Highlight): The wise man told them to switch camels. This would allow the fastest son to win.
Red and Blue - Logic Puzzle
Monday, May 4, 2009
3 boxes of marbles sit in front of you, all of them are mislabeled.
Box 1 reads : Red
Box 2 reads : Blue
Box 3 reads : Red and Blue
Only removing one marble from one box, without knowing any other contents of the box, can you correctly place the labels?
Solution (Highlight): Remove one marble from the 3rd box. If it is red, move label 1(Red) to label 3. Because Box 2 is labeled incorrectly it must be Red and Blue. That leaves Box 1 to be Blue.
Journey - Logic Puzzle
A man runs a mile south, a mile west, and a mile north and ends up back where he started!
Where must he have begun his journey?
Solution (Highlight):
You begin your journey so that after you walk 1 mile south you are 1/2pi miles from the south pole. Then when you walk 1 mile west you end up where your circle started and can walk 1 mile north to your original starting location.
Light Bulbs - Logic Puzzle
There are three switches in front of you. Each corresponds to one of the three light bulbs in the next room. You can turn the switches on or off and leave them in any position.
How would you identify which switch corresponds to which light bulb, if you are only allowed to enter the next room once?
Solution (Highlight):
First, turn the first light switch on for an extended period of time. Then, turn it off.
Turn the second switch on and leave the third switch off.
Move into the next room. The bulb that is on will be the second switch and the bulb that is hot and off will be connected to the first switch.
