Saturday, April 30, 2016

Welcome to Oklahomainewmexiconnecticutah!

1. Which state name is last alphabetically?

Wyoming

2. Which state name ends in three vowels?

Hawaii

3. Which state names begin and end with the same letter? (4)

Alabama, Alaska, Arizona, Ohio

4. Which two state names end with the letters LAND?

Maryland, Rhode Island

5. Which state names have a double letter? (9)

Connecticut, Hawaii, Illinois, Massachusetts, Minnesota, Mississippi, Missouri, Pennsylvania, Tennessee

6. True or False? Every letter of the alphabet is needed to write the names of the fifty states.

False: You don't need Q.

7. Which state names could be spelled out very nicely in capital letters using toothpicks because none of the letters are curved? (2)

HAWAII, MAINE

8. Which state name has the fewest syllables?

Maine

9. Which one-word state name has the most syllables?

Louisiana has five syllables—unless you live there!

10. Do more state names end with a vowel or end with a consonant? (Take bets first!)

More state names end with a vowel.

11. Do more state names begin with a vowel or begin with a consonant?

More state names begin with a consonant.

12. One day, the citizens of Florida and the citizens of Idaho noticed that the last part of "Florida" is the first part of "Idaho." So they voted to become one state, Floridaho! Can you think of any other states that could vote to unite because of matching first and last parts?

Looking only for matching parts that have two or more letters, I found these possibilities:

Vermont, Montana → Vermontana
Wisconsin, Indiana → Wisconsindiana
Alabama, Maryland → Alabamaryland
Ohio, Iowa, Washington → Ohiowashington
Oklahoma, Maine, New Mexico, Connecticut, Utah → Oklahomainewmexiconnecticutah

13. I once drove a car through three consecutive states all beginning with the same letter. What were the states?

Iowa, Illinois, Indiana

14. If you want to leave this state by crossing the border into the state that immediately follows it in alphabetical order, you can do that - but only if you're on a boat. What state is it?

Michigan

15. The only two states that have this letter in their name also happen to share a border. What letter is it?

X

16. Starting out from this state, I can drive due north, or due west, and in either case enter a state that has no letters in common with the state where I started. In what state did I start?

Alabama. (Drive north into Tennessee, or drive west into Mississippi.)

Tuesday, April 26, 2016

Fifty-State Word Games

I made these puzzles during a family vacation when my kids were getting antsy and needed something to do. (It was my wife who got the ball rolling by proposing #5.)

For reference, I gave the kids an alphabetized list of state names. Puzzles 13-16 also call for a map. Supply copious hints as needed!

1. Which state name is last alphabetically?

2. Which state name ends in three vowels?

3. Which state names begin and end with the same letter? (4)

4. Which two state names end with the letters LAND?

5. Which state names have a double letter? (9)

6. True or False? Every letter of the alphabet is needed to write the names of the fifty states. 

7. Which state names could be spelled out very nicely in capital letters using toothpicks because none of the letters are curved? (2)

8. Which state name has the fewest syllables? 

9. Which one-word state name has the most syllables?

10. Do more state names end with a vowel or end with a consonant? (Take bets first!)

11. Do more state names begin with a vowel or begin with a consonant?

12. One day, the citizens of Florida and the citizens of Idaho noticed that the last part of "Florida" is the first part of "Idaho." So they voted to become one state, Floridaho! Can you think of any other states that could vote to unite because of matching first and last parts?

13. I once drove a car through three consecutive states all beginning with the same letter. What were the states?

14. If you want to leave this state by crossing the border into the state that immediately follows it in alphabetical order, you can do that - but only if you're on a boat. What state is it?

15. The only two states that have this letter in their name also happen to share a border. What letter is it?

16. Starting out from this state, I can drive due north, or due west, and in either case enter a state that has no letters in common with the state where I started. In what state did I start?


Sunday, April 24, 2016

BAA to WRY in 32 Steps

In this post, I'll show the promised long chain from BAA to WRY. To make contact with where we began, I'll recast the problem as an Alphabet Slider.


Right now, the sliders indicate the word BAA. If you move the sliders down far enough, you can indicate the word WRY.

So here's the game: how many words can you form by moving sliders downward? The game is over when the sliders finally indicate WRY.

Note, on each play, exactly one slider moves down.

(For the answer I found using a computer, scroll down.)




























BAA
BAD
BAG
BAH
BAM
BAN
CAN
CAP
CAR
EAR
FAR
GAR
GAS
HAS
HAT
HAW (fruit of a hawthorn)
JAW
LAW
LAX 
LAY
MAY
NAY
PAY
RAY
SAY
SHY
SKY
SLY
SOY
TOY
TRY
WRY

This solution leaves the central A in place for a very long time, eventually harvesting a run of six -AY words before finally taking advantage of the possibilities afforded by the initial letter S to branch out at the middle position.

Here's what the endgame looks like as a graph. Each vertex is a word, and an arrow points from one vertex to another if it is a fair play to change the first word into the second. (I removed direct shortcuts from the graph.) Sorry the word labels aren't visible—LAX is at the top, and TRY is at the bottom.






Thursday, April 21, 2016

Directional Change-A-Word

Inspired by reader mdahlman's comment on the Alphabet Slider puzzle, I came up with this variation on the traditional "Change-A-Word" puzzle:

BAA

WRY
Change one letter at a time until BAA becomes WRY. Each intermediate step must be a valid word. You may only change a letter into one that occurs later in the alphabet. 
I was able to do this in four steps. Can it be done in three?

At the other extreme, the most meandering solution that I could find has 31 steps. (I found it using a computer.) I'll share it next time.

***

Some notes:

(1) This game isn't equivalent to the one mdahlman had in mind, because only one letter at a time can change.

(2) A long time ago, I reported that in the standard Change-A-Word game, most four-letter words can be reached from most four-letter words. Four-letter words are like a vast, connected raft, or continent, with just a few isolated offshore islands. Here's the largest of the islands:


In a comment on that post, reader danimal suggested a variation on Change-A-Word in which the player may only change a given letter to a letter adjacent to it in the alphabet. I found it difficult to create instances of that version of the game, but the upshot of the present post is that we get plenty of instances if we replace the adjacency requirement with a directional requirement.

Saturday, April 9, 2016

Alphabet Slider, Cont'd

The slider mechanism in the Alphabet Slider puzzle determines what's called a "partial ordering" on three-letter words. Specifically, given two words w1 and w2, we write

w1 < w2 

if every letter of w1 occurs earlier in the alphabet than the corresponding letter of w2. For example, we write

ACE < PYX

because A is earlier in the alphabet than P, C is earlier in the alphabet than Y, and E is earlier in the alphabet than X.

There exist words "between" ACE and PYX. For example,

ACE < EON < PYX

as you can check. A solution to the Alphabet Slider is a chain like the one above, and the goal is to find the longest possible chain. With the help of a computer, I found this solution:

ACE < BEG < CHI < DIM < EON < FRO < ITS < JUT < PYX.

(An equally long chain results from using NUT instead of JUT. A reader also notes that OUT could go in this position.)

Here's a picture—note that lines never cross.

The game can be played with words of any length. For example, here's a pretty good chain of four-letter words:

ABBE < DILL < ELMS < FONT < GROW < JURY.

For eight-letter words, I found

HEADACHE > KNEELING > SPONSORS.

Thursday, April 7, 2016

Alphabet Slider

This is a puzzle about three-letter words. Right now, the sliders indicate the word ACE. If you move the sliders down far enough, you can indicate the word PYX.

(Definition of PYX here; FWIW, I first learned the word here.)

So here's the game: how many words can you form by moving sliders downward? The game is over when the sliders finally indicate PYX.

Note, sliders aren't allowed to stay put; on each play, all three sliders have to move down.

Thursday, March 24, 2016

Solution to Ne-Rd-Y B-Ra-In Te-As-Er

Tin, an element in the periodic table, can be spelled using abbreviations from the periodic table: (Ti)(N).

What other elements can you find with this property?

As listed in the previous post, there are 118 element names in all, of which 85 end in the letters -ium or -um. None of those 85 can be spelled using abbreviations from the periodic table, because there aren't any elements abbreviated M, Um, or Ium.

The remaining 33 elements are:

antimony, argon, arsenic, astatine, bismuth, boron, bromine, carbon, chlorine, cobalt, copper, fluorine, gold, hydrogen, iodine, iron, krypton, lead, manganese, mercury, neon, nickel, nitrogen, oxygen, phosphorus, radon, silicon, silver, sulfur, tin, tungsten, xenon, zinc.

Of these, 13 can be spelled using element abbreviations:

carbon, neon, silicon, phosphorus, iron, copper, arsenic, krypton, silver, tin, xenon, bismuth
astatine.

By the way, the big story this year for periodic table junkies was the certification of elements with Z = 113, 115, 117, and 118 by the relevant IUPAC/IUPAP Joint Working Party. The process of giving those elements permanent names now begins.