Halloween Special: Your Favorite Problems
Oct 31st, 2006 by Percy
Here are some of your (and our) favorite problems. Enjoy — trick or treat!
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Problem One: Gadsby
If youth, throughout all history, had had a champion to stand up for it; to show a doubting world that a child can think; and, possibly, do it practically; you wouldn’t constantly run across folks today who claim that “a child don’t know anything.” A child’s brain starts functioning at birth; and has, amongst its many infant convolutions, thousands of dormant atoms, into which God has put a mystic possibility for noticing an adult’s act, and figuring out its purport.
What’s significant about this quotation from a book (and this conundrum)?
Source: Gadsby by E. V. Wright
Problem Two: Thrifty Thugs
Five thugs steal 100 diamonds. They come up with a way to distribute them. They get in line and the first thug suggests a sharing method. Then, a vote is taken. If more than 50% agree, the method is used. Otherwise, the suggester is killed and the next person in line suggests another solution. Assuming all five people are intelligent and self-serving, what are the end results?
Problem Three: Estmodus Inrebus
Since this is quite a tough problem, I’m not going to post nine more problems today, and I hope everyone try this because it is actually really interesting.Replace the letters and asterisks with digits to satisfy the multiplication:
Don’t ask me what “Estmodus Inrebus” means. I have no clue. FYI this puzzle comes from “The Master Book of Mathematical Recreations” created by a mathematician by the name of Fred Schuh. I’ll try to post a full solution to this problem in a few days.
Edit: I just found out what the phrase means. It’s actually “Est modus in rebus”, a quote from Horace (Ancient Roman poet), meaning “There is a measure in things”.
Problem Four: The Four Doors
A man wakes up in a room. He sees no windows, a table with a note on it, and four doors ahead of him. Each door has a different symbol on its face: rectangle, kite, rhombus, and trapezoid.He then walks to the table and reads the message:
“Three of these doors hold behind them a deadly booby trap, and one of them leads to the exit of this house. You can only open one door. The door that leads to the exit of this house can be deduced by looking at a string of numbers hidden somewhere in the house. Figure it out quickly, however, because as soon as the clock strikes noon, all the doors in the house will become permanently locked.”He then searched everywhere in the room, until he found a string of numbers carved under the table:1 - 4 - 8 - 11 - 1He thought long and hard as the clock ticked away, getting closer and closer to his potential doom.Suddenly he realized what the numbers meant, and promptly went over to the correct door, which he opened and managed to escape the house unhindered.
Which door leads to the exit?
Problem Five: Mayhen
If a hen and a half lays an egg and a half in a day and a half, how many and a half who lay better by half will lay half a score and a half in a week and a half?
Source: 536 Puzzles and Curious Problems by Dudeney (p. 50)
Problem Six: The Blind Mathematician
Here’s is a fun problem I found on the Internet today while browsing around:
Once upon a time a king wanted to hire the best Mathematician in his kingdom to work in his palace. His servants brought to him the best two mathematicians, one of them was blind. The king told both mathematicians that he can’t hire both so he will ask a question and whoever answers gets the job.
The king said: “I have three sons, whoever guesses their ages will be hired.” The king told them that if they multiply the ages of his sons the result will be 36. Both mathematicians told the king that this information is not enough. The king then said: “The number of windows in the building across the street is equal to the sum of the ages of my sons.” The first mathematician (who can see) counted the windows, and told the king that he still could not figure it out. The Blind mathematician (who could not count the windows) told the king that he does not have an answer. The king then said: “My oldest son has red hair.” Right away the blind mathematician gave the correct answer and got hired.
The question is: How did the blind guy know the answer and what is the answer?
There are no ‘tricks’ to this problem. An you can assume the age are whole numbers and if their ages differ by less than a year they count as having the same ages (i.e. two six year olds have the same ages regardless of when they are born).
Problem Seven: 16 Coins
Johnny was given 16 coins by his older, somewhat meaner brother, Mark. He told him that he could keep them all if he could place all 16 on the table in such a way that they formed 15 rows with 4 coins in each row.After 10 minutes, Johnny walked away with the coins and Mark, after complaining futilely to his mother, left with nothing.How did Johnny place the coins?
Problem Eight: Connect the Dots II
Go through all 49 dots in twelve straight contiguous lines. Begin and end on the red dot.
Problem Nine: Eating for Free?
A family of eight were eating at a nice hometown diner. After all of them had their fill of grub, they received the bill. The bill ended up being exactly $69.69, but the family left the diner without paying a dime. They were not arrested for not paying the bill, in fact, their waitress wished them a good night before they left. How did they get away with a seemingly free meal?
Problem Ten: Critical Moment
This is probably one of the most famous puzzles of all time, but I’ll post it here anyways in case someone hasn’t seen it before.In a game show you can pick one of three doors. A,B or C. One of the doors holds the car you got your eyes on. The others contain goats. You guess door A. The host (knowing which door holds the prize) opens one of the 2 other doors that he knows holds no prize. He opens door B. He tells you to try again, and pick one of the 2 doors that are left, A or C. Which door should you pick?
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