The Puzzling Martin Gardner
This Monday’s puzzles are straight from the pen of Martin Gardner.
Happy Scheming.
(image: Gilbert Jain Photography)
Question 1
In a certain African village there are 800 women. Three percent of them are wearing one earring. Of the other 97 percent, half are wearing two earrings, half are wearing none. How many earrings altogether are being worn by the women?
Question 2
(From Samuel Taylor Coleridge’s private notebooks, paraphrased):
Suppose you gather a certain number of apples in a particular orchard. This orchard has three guarded gates, through which you must pass. To the guard of the first gate, you give half of the apples you have, plus half an apple. To the guard of the second gate you pass, you give half of the remaining apples, plus half an apple. And to the guard of the third gate, you give half of what’s left, plus half an apple. How many apples did you initially gather if at the end of this process you have no apples left and you’ve cut none of the apples in half.
Question 3
A rose-red city half as old as Time.
One billion years ago the city’s age
Was just two-fifths of what Time’s age will be
A billion years from now. Can you compute
How old the crimson city is today?
Question 4
An absent-minded bank teller switched the dollar and cents when he cashed a check for Mr. Brown, giving him dollars instead of cents, and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had left exactly twice as much as his original check. What was the amount of the check?
Question 5
If one penny rolls around another penny without slipping, how many times will it rotate in making one revolution?
Question 6
A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes. What is the minimum number of cuts required to do this?
Question 7 – I LOVE THIS ONE!
During a baseball game in Mudville, Casey was Mudville’s lead-off batter. There were no substitutions or changes in the batting order of the nine Mudville men throughout the nine-inning game. It turned out that Casey came to bat in every inning. What is the least number of runs Mudville could have scored?
For Number 1:
there are 800 earrings. each of the women averages to wearing one.
Yup, that’s right Mr. Mouse.
Hey, it’s noon already and Tien and Lynh haven’t yet answered every question. Is this bizarro-world?
Sorry … I totally forgot about puzzles today.
2) Am I missing a beat but doesn’t that just mean that he took no apples?
3) The Crimson City is 7 billion years old.
4) The amount of the check was $31.63.
5) It will rotate once.
6) six cuts
7) 8 runs?
5) 2 times
7) I got 16 runs
Ah, answer attempts! Beautiful.
Okay, for #2, there are not zero apples. The answer is 7. Half of seven plus half is 4, leaving 3. Half of three plus half is 2, leaving 1. Half of 1 plus half is 1, leaving none.
#3: Correct, 7 billion years old.
#4: Correct, $31.63
#5: Correct (Chris): it will rotate twice.
#6: Correct, 6 cuts. (the cube in the center is proof).
Now, for my favourite, number seven, Casey at the Bat.
The answer is ZERO, that’s right, NONE.
In the first inning, Casey comes to bat. He walks, and the next two batters walk. The next three batters strike out.
In the second inning, the first three men walk, bringing Casey to the plate. The pitcher proceeds to pickoff all three baserunners, meaning, Casey leads off in the next inning (the third).
This process is continued until the end of the game.
There is no joy in Mudville!
Are you kidding me…a handful of my man Martin and I’m asleep at the wheel. Arrrrrgh.
Number 7 ain’t so crazy- in 1983 three blue Jays were picked off of first by Tippy Martinez in the 10th inning of a game against Baltimore. They were rather eager to steal because Baltimore had pulled both their catchers and had a reserve infielder behind the plate (not to mention outfielders playing 2nd and 3rd) . Then the guy filling in at catcher hit a home run in the bottom of the 10th to win it. Ouch.