Gathering For Gardner: Celebration of Mind

On October 21st, 1914, the great American mathematics writer and popularizer, Martin Gardner was born.  While not a mathematician himself, Gardner’s popular works inspired a generation of young people to pursue mathematics with his great efforts to bring recreational mathematics into the American home.  From 1956 to 1981, he wrote the Mathematical Games column in Scientific American and over the course of his long career, authored more than 70 books (not just limited to recreational mathematics; he was also a great friend to sceptics).

Since Martin Gardner was notoriously shy and often would choose not to attend awards ceremonies honouring him, in 1993, a puzzle collector by the name of Tom Rodgers convinced him to attend an event devoted to mathematical puzzle solving.  The event was held again in 1996, and again attended by Gardner (for the second and final time), and has since become a semi-annual-tradition, being held near Atlanta.  The program for this event, called Gathering for Gardner, consists of any topic which Gardner wrote on during his career.

In May of this year, Gardner passed away at the age of 95.  While he wanted no memorials* in his honour, he did want the Gatherings for Gardner to continue.  This year, the first gathering since his death, the Martin Gardner Global Celebration of Mind Gatherings will take place in dozens of different locations around the world, on October 21st, 2010 (on what would have been Gardner’s 96th Birthday).

To celebrate Gardner’s work and life, and to share in his love for mathematics, science, magic and puzzles, the G4G Foundation is encouraging everyone to perform a magic trick, share a puzzle or recreational mathematics problem with friends.

In a week where New York Magazine publishes an anti-math article on “ridiculous sounding” popular mathematics classes, I think the world needs a little dose of recreational mathematics, and to remember how fun and exciting Gardner made mathematics for the general public.

Puzzles for Gardner

Many of these originally appeared in Gardner’s Scientific American column, if you want solutions, I can post those next week (although Google should be able to find the answers to any people can’t get).

1. You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.  How can you identify which one is a magnet?

2. Write out the alphabet starting with J (like: JKLMNOPQRSTUVWXYZABCDEFGHI).  Erase all letters that have left-right symmetry (such as A) and count the letters in each of the five groups that remain.

3. Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?

4. A logician vacationing in the South Seas finds himself on an island inhabited by the two proverbial tribes of liars and truth‐tellers. Members of one tribe always tell the truth; members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truthteller or liar. The logician thinks a moment and then asks one question only. From the reply, he knows which road to take. What single yes/no question does he ask?

5. Make a single cut (it needn’t be straight) to divide the brownie below into two identical pieces.

6. A woman either always answers truthfully, always answers falsely, or alternates true and false answers. How, in two questions, each answered by yes or no, can you determine whether she is a truther, a liar, or an alternater?

7. Two missiles speed directly toward each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start 1,317 miles apart. Without using pencil and paper, calculate how far apart they are one minute before they collide.

8. Can you change the giraffe into a different giraffe by moving just one toothpick?

9. Family planning. A Family of four (father, mother, son, and daughter) went on a hike. They walked all day long and, when evening was already drawing on, came to an old bridge over a deep gully. It was very dark and they had only one lantern with them. The bridge was so narrow and shaky that it could hold no more than two persons at a time. Suppose it takes the son 1 minute to cross the bridge, the daughter 3 minutes, the father 8 minutes, and the mother 10 minutes. Can the entire family cross the bridge in 20 minutes? If so how? (When any two persons cross the bridge, their speed is equal to that of the slower one. Also the lantern must be used while crossing the bridge.)

10.

For more math puzzles try Cliff Pickover or the G4G Hosting site.

*Scientific American did do an excellent tribute piece for Gardner after his death.

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9 Responses to Gathering For Gardner: Celebration of Mind

  1. Flavin says:

    I liked #6. It’s a twist on #4 that I had never heard. I think I figured out a solution that would not only distinguish liar, truther, and alternater, but would tell you whether the alternation started on a lie or a truth.

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  3. Eddie says:

    1. You are in a room with no metal objects except for two iron rods. Only one of them is a magnet. How can you identify which one is a magnet?

    Use one to try to pickup the other?

    2. Write out the alphabet starting with J (like: JKLMNOPQRSTUVWXYZABCDEFGHI). Erase all letters that have left-right symmetry (such as A) and count the letters in each of the five groups that remain.

    Too much work.

    3. Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?

    1/3 and 1/2 ? i really should remember how to do this… : (

    4. A logician vacationing in the South Seas finds himself on an island inhabited by the two proverbial tribes of liars and truth‐tellers. Members of one tribe always tell the truth; members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truthteller or liar. The logician thinks a moment and then asks one question only. From the reply, he knows which road to take. What single yes/no question does he ask?

    Ask him if the path in question (left or right) is the way to his village.

    5. Make a single cut (it needn’t be straight) to divide the brownie below into two identical pieces.

    I’d like a brownie right now.

    6. A woman either always answers truthfully, always answers falsely, or alternates true and false answers. How, in two questions, each answered by yes or no, can you determine whether she is a truther, a liar, or an alternater?

    Ask her if she is a woman twice.

    7. Two missiles speed directly toward each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start 1,317 miles apart. Without using pencil and paper, calculate how far apart they are one minute before they collide.

    1317 miles?

    8. Can you change the giraffe into a different giraffe by moving just one toothpick?

    I can make it a male giraffe with another toothpick.

    9. Family planning. A Family of four (father, mother, son, and daughter) went on a hike. They walked all day long and, when evening was already drawing on, came to an old bridge over a deep gully. It was very dark and they had only one lantern with them. The bridge was so narrow and shaky that it could hold no more than two persons at a time. Suppose it takes the son 1 minute to cross the bridge, the daughter 3 minutes, the father 8 minutes, and the mother 10 minutes. Can the entire family cross the bridge in 20 minutes? If so how? (When any two persons cross the bridge, their speed is equal to that of the slower one. Also the lantern must be used while crossing the bridge.)

    Took me about 5 minutes to do this so my family would not have made it in time. D&S -> 3 min / S 10 min / D 3 min.
    Thats 20 min but my 5 minute thinking put it at 25 min irl. So I LOSE!

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