No answers? OK. (BTW, this is from Martin Gardner's 6th Book of Mathematical Diversions from Scientific American)
Under the conditions stated, it's actually possible to have as few as 0 runs by the 9th inning:
1st inning: Casey, and the two batters following him, all walk. The next three strike out, so the inning is over.
2nd inning: The first 3 walk again, and Casey comes up to bat. However, before Casey even gets to swing at a ball, each of the three runners are caught by the pitcher off base, resulting in 3 outs, and the inning is over.
3rd inning: Casey starts this inning still at bat (thanks to the pick-off play in the 2nd inning), and the process from the 1st inning and the 2nd inning can be repeated from here for the remainder of the game.
1. In 1978, Raymond Smullyan wrote a book about logical puzzles. What is the name of this book?
2. I am the square root of -1. Who am i?
3. What would the value of 190 in hexadecimal be?
4. Twenty-nine is a prime example of what kind of number?
5. The reciprocal ofis half of what number?
6. How many consonants are in "one"? How many in "two"? And how many in "three"?
7. What do you do to the length of an edge of a cube to find its volume?
These questions are based on the principle of self-recursion. To learn more about self-recursion, click here.
Here's a challenge focusing on Casey at the Bat (full poem below). Assume that, during that famous game, there were no substitution of players, and there were also no changes in the Mudville line-up. Further, assume that, because of his star status and ability, that Casey is the team's lead batter, and that he's been up to bat each inning.
Under those conditions, is it possible, as in the poem, for Mudville to have only 2 points by the last inning? What is the fewest number of runs that Mudville could have scored under those conditions?
Casey at the Bat
by Ernest Lawrence Thayer
Published: The Examiner (06-03-1888)
The Outlook wasn't brilliant for the Mudville nine that day:
The score stood four to two, with but one inning more to play.
And then when Cooney died at first, and Barrows did the same,
A sickly silence fell upon the patrons of the game.
A straggling few got up to go in deep despair. The rest
Clung to that hope which springs eternal in the human breast;
They thought, if only Casey could get but a whack at that -
We'd put up even money, now, with Casey at the bat.
But Flynn preceded Casey, as did also Jimmy Blake,
And the former was a lulu and the latter was a cake;
So upon that stricken multitude grim melancholy sat,
For there seemed but little chance of Casey's getting to the bat.
But Flynn let drive a single, to the wonderment of all,
And Blake, the much despis-ed, tore the cover off the ball;
And when the dust had lifted, and the men saw what had occurred,
There was Jimmy safe at second and Flynn a-hugging third.
Then from 5,000 throats and more there rose a lusty yell;
It rumbled through the valley, it rattled in the dell;
It knocked upon the mountain and recoiled upon the flat,
For Casey, mighty Casey, was advancing to the bat.
There was ease in Casey's manner as he stepped into his place;
There was pride in Casey's bearing and a smile on Casey's face.
And when, responding to the cheers, he lightly doffed his hat,
No stranger in the crowd could doubt 'twas Casey at the bat.
Ten thousand eyes were on him as he rubbed his hands with dirt;
Five thousand tongues applauded when he wiped them on his shirt.
Then while the writhing pitcher ground the ball into his hip,
Defiance gleamed in Casey's eye, a sneer curled Casey's lip.
And now the leather-covered sphere came hurtling through the air,
And Casey stood a-watching it in haughty grandeur there.
Close by the sturdy batsman the ball unheeded sped-
"That ain't my style," said Casey. "Strike one," the umpire said.
From the benches, black with people, there went up a muffled roar,
Like the beating of the storm-waves on a stern and distant shore.
"Kill him! Kill the umpire!" shouted someone on the stand;
And its likely they'd a-killed him had not Casey raised his hand.
With a smile of Christian charity great Casey's visage shone;
He stilled the rising tumult; he bade the game go on;
He signaled to the pitcher, and once more the spheroid flew;
But Casey still ignored it, and the umpire said, "Strike two."
"Fraud!" cried the maddened thousands, and echo answered fraud;
But one scornful look from Casey and the audience was awed.
They saw his face grow stern and cold, they saw his muscles strain,
And they knew that Casey wouldn't let that ball go by again.
The sneer is gone from Casey's lip, his teeth are clenched in hate;
He pounds with cruel violence his bat upon the plate.
And now the pitcher holds the ball, and now he lets it go,
And now the air is shattered by the force of Casey's blow.
Oh, somewhere in this favored land the sun is shining bright;
The band is playing somewhere, and somewhere hearts are light,
And somewhere men are laughing, and somewhere children shout;
But there is no joy in Mudville - mighty Casey has struck out.
Of course, there's the old gag of simply saying the phrase "Z to A backwards!"
I've done this so much, I can teach anybody else to do it in about 5 minutes.
Just for fun, I also learned to say the alphabet backwards and forwards simultaneously (Starting with Z, the A, then Y, then B, and so on):
My name is Scott, and I've just joined.
My main interests are recreational mathematics, puzzles, and memory techniques.
I run two blogs. The main one (the largest) of the two is Grey Matters ( http://headinside.blogspot.com/ ), which concerns recreational math, magic, and memory. The other one, which focuses exclusively on puzzles related to current events, is Scott's Puzzles ( http://puzzlescott.blogspot.com/ ).
I've run across the Math Is Fun Forum before, but I finally looked through it enough to decide to register.
Thank you for putting this forum up!
For the planets, I had always learned:
My Very Easy Method Just Speeds Up Naming Planets
To remember the English Monarchs, there's:
Willie, Willie, Harry, Stee,
Harry, Rich, John, Harry Three,
One-To-Three Neds, Richard Two,
Harrys Four-Five-Six... then who?
Edwards Four-Five, Rich the Bad,
Harrys (twain), Ned Six (the lad),
Mary, Bessie, James you ken,
Then Charlie, Charlie, James again...
Will & Mary, Anne of gloria,
Georges ( 4! ), Will Four, Victoria,
Edward Seven next, and then
Came George the Fifth in 1910...
Ned the Eighth soon abdicated,
So George Six was coronated,
Then Number Two Elizabeth...
And that's all, folks (until her death...)!!
Eventually, the last line is expected to be changed to:
Charles Three (and now I'm out of breath...!)
If I asked you to arrange the numbers 1-9, used only once each, in a 3 by 3 grid so that the first two rows add up to the 3rd, you might come up with any one of several answers. For example, you might come up with this answer:
This is a correct answer, because all the numbers 1-9 are used, and 354 + 618 = 972.
Let's say I instead ask you to arrange the numbers 1-9 in a 3 by 3 grid so that a chess rook, which can only move horizontally or vertically, could be placed on the number 1, and travel in sequence up to the number 9 using only legal rook moves. This is also a fairly easy puzzle, and there are several answers, including the following one:
In that particular arrangement, you would place the rook on the 1, move it vertically to the 2, then the 3, then do a horizontal move to the 4, move up vertically to the 5 and the 6, and then a horizontal move to the 7, which allows you to conclude by moving down vertically through the 8 to the 9.
Each of the above puzzles is fairly simple on its own, so let's make it more challenging by combining them. Can you arrange the numbers 1-9 in a 3 by 3 grid so that the top two rows add up to the third row AND so that a rook can be placed on the number 1, and moved, using only legal rook moves, to each number sequentially, and finishing on the 9?