Blaine's Puzzle Blog

NPR Sunday Puzzle (Jun 12, 2011): Sam Loyd's Hat Rack Puzzle

2011-06-16T12:00:00.000-07:00

NPR Sunday Puzzle (Jun 12, 2011): Sam Loyd's Hat Rack Puzzle:

This Hat Rack Puzzle by Sam Loyd was published 100 years ago in Woman's Home Companion:

Q: A hat room contains a wall with 49 pegs, arranged in a 7-by-7 square. The hat clerk has 20 hats that are to be hung on 20 different pegs. How many lines, containing four hats in a straight line, is it possible to produce? A line can go in any direction: horizontally, vertically or obliquely. To explain your answer, number the pegs in order, from 1 in the upper left corner to 49 in the lower right corner; list which pegs you put the 20 hats on, and give the total number of lines containing four hats in a row.

Liane has left, but it also seems like the NPR website editors are gone. Last week they had "goose" as a two word phrase (instead of "roast goose") and this week they misspelled Sam Loyd (as Sam Lloyd). Anyway, back to the puzzle; not counting rotations and reflections, I have 3 ways to get the answer.

Edit: If you re-read my post you'll see the phrase "are gone" at the end of the first sentence. This is a homphone of Argon with atomic number 18, a clue to there being 18 lines in the solution(s).

A: I found 3 main solutions (not counting reflections and rotations). Click each one to see a larger view with any rotated/reflected variants.

Write the Alphabet Backwards, Quicker than Forwards!

2011-01-18T17:40:00.000-08:00

I was reminded recently of a way to impress your friends and perhaps win a bet too. It involves writing the alphabet backwards faster than they can forwards.

The key is to learn the backwards alphabet as "words" rather than individual letters. If you break it into chunks of 4 letters (with 2 left over) you have:

ZYXW VUTS RQPO NMLK JIHG FEDC BA
Phonetically think of this as the phrase:
"Zixwa Vuts Irqpo Nimlick Jig Fedic Bah"

Practice saying this as you write each set of letters one after the other. With a little practice you'll be able to write this very quickly.

Now you are ready to challenge your friends to a race. You can even bet them that you'll write the alphabet backwards faster than they write it forwards. The reason it works is you won't need to stop, think, sing that alphabet song, go back a few letters, etc. You simply write down your 7 "words" as quickly as possible and you are sure to beat them.

Enjoy!

Hack the Video Password, by Solving our Christmas Puzzle

2010-12-21T23:19:00.000-08:00

This year we've hidden a secret video message as the solution to our puzzle. Only those that can spot the 8 differences in our annual Christmas Puzzle will be able to figure out the password. Are you up to the challenge?

Note: If you need some help there are hints on the puzzle page and even the complete solution, but try solving it without help first... it's more fun that way.

When you solve it, please don't give away the answer but feel free to add a comment to let us know that you successfully figured it out. And we are always looking for new ideas for next year's Christmas puzzle, so submit those too.

Friday Fun: Rapidly Rotating Electronic Lock

2009-05-01T00:34:00.000-07:00

It's Friday and you are looking forward to the weekend, but an evil genius has locked you in a room. The door to the room is protected by a special electronic lock with four identical buttons equally spaced along the rim of a circular dial.

Each button toggles an internal switch within the mechanism. You can attempt to open the lock by simultaneously pressing any set of the 4 buttons which will toggle the corresponding switches. If you are lucky enough to thereby align the switches so they are all on or all off, the lock will open. Otherwise the dial begins a spinning cycle that lasts for 1 full minute. When it comes to rest you have no way of knowing which button(s) you pressed previously.

Your captor is returning in 15 minutes. Is there any possible method you can think of that will GUARANTEE that you can open the lock in less than 15 tries? If it is not possible, then let me know why that is the case... so I don't waste my time.

Friday Fun: What's the next number in the sequence?

2009-03-27T17:55:00.000-07:00

Can you figure out the next few terms in the following sequence?

Q: 1, 3, 7, 12, 18, 26, 35, 45, 56, 69...

I'll post the answer some time next week.

Word Game: If I give you BVI, the answer is obvious...

2009-02-11T07:27:00.000-08:00

Here's a fun game you can play with friends. I'll give you a sequence of letters. Your goal is to find a common English word that has those letters exactly in that order with no additional letters in between. As the title implies, if I gave you "BVI" you could reply with "oBVIous". Got it?

To get you started, here are a few combinations to try:
HTG, WKW, UMF, PTC, GGP, AUE and HMM...

Good luck, and feel free to post any letter combinations of your own that might be fun to try.

New Year's Resolution: Exercise Your Brain

2009-01-02T05:17:00.000-08:00

As long as everyone is making New Year's resolutions, I hope you've made one to get more mental exercise. To start you off, here's a challenging "Cross Number Puzzle." The grid above is filled in like a traditional crossword puzzle, except every answer is a three-digit number (100-999) rather than a word. Warning: some of the clues may have you going in circles but there is a unique solution..

Click here for a printable version of the puzzle. And don't worry, you can get around to your other resolutions, like not procrastinating, and going to the gym later. Go sit on the sofa and work on a puzzle instead!

Across:
1. 3 Down plus 5 Across
3. One-seventh of 8 Across
5. Half of 14 Across
6. A prime number
8. Seven times 3 Across
10. Twice 7 Down
12. A perfect square
14. 9 Down reversed
15. The sum of its own digits, times thirty-seven
16. A perfect square

Down:
1. 13 Down plus 10 Down
2. Average of 9 Down and 14 Across
3. 1 Across minus 5 Across
4. A multiple of three
7. 16 Across minus 1 Across
9. 1 Across plus 5 Across
10. 13 Down plus three hundred
11. 12 Down minus 1 Down
12. Anagram of 4 Down
13. 1 Down minus 10 Down

Can you solve our Colorful Christmas Crossword (2008)?

2008-12-26T19:15:00.001-08:00

This year's Christmas puzzle is a fun, themed crossword. And there is a secret holiday surprise if you are able to solve it. Take a look at our Christmas Puzzle for 2008.

Note: if you need some hints on solving the puzzle, post your questions here. But please don't give away any of the secrets, especially the final solution website address.

Friday Fun - Mini-Sudoku Puzzle (nine squares!)

2008-09-26T17:36:00.000-07:00

For all of those that are tired of having to fill in a full Sudoku grid, here's a Mini-Sudoku Puzzle. The goal is to fill the nine squares with just the digits 1 to 9. The only hints provided are the "L-block" hints at each corner. Each value tells you the sum of the five squares that make up the two adjacent edges.

Note: This is not a magic square. You cannot make any assumptions about the totals of the rows, columns or diagonals.

See how quickly you can come up with the unique solution. I'll probably post the answer next Friday. In the meantime, please don't reveal the answer so others can enjoy the puzzle too. Post comments on whether you find this puzzle easy, hard, fun or frustrating. I'd be interested in your solving techniques and times, too.

Friday Fun - Cycling on the Bridge

2008-08-01T06:29:00.000-07:00

Two bicyclists start cycling from opposite ends of a bridge. One cyclist is faster than the other and they meet at a point 2,000 feet from the nearest end. When each cyclist reaches the opposite end of the bridge, he takes a 15 minute rest break and then starts on his on return trip. The cyclists again meet 720 feet from the other end. Assuming each is cycling at a constant speed, how long is the bridge?

Note: There is no mention of the actual speed of each cyclist, or the time that each takes but this problem is solvable. In fact, there is an elegant solution that could be understood by an elementary school student, with basic rules of addition and subtraction. It can also be solved the "hard" way. I'll post the elegant solution next week.

Edit: I've provided an answer in the comments.

Friday Fun - How Long is the Ring Road around Iceland? - Answer

2008-07-25T08:00:00.000-07:00

We should be flying back home from Iceland about this time. Hopefully everyone has had fun with the puzzles while we have been gone. If you haven't had a chance to solve the puzzle about the Iceland Ring Road yet, take a look at last Friday's post and don't read any further. But if you want the answer, read on...

A: Let A be the speed of the first couple and B be the speed of the second couple. After an equivalent amount of time T, one couple has traveled AT miles and the other travels BT miles. For the return, the first couple now travels BT miles in 9 hours, while the other couple travels AT miles in 16 hours.

A = BT/9
B = AT/16

9A = BT
16B = AT

T = 9A/B
T = 16B/A
9A^2 = 16B^2
Take the square root of both sides (which is okay because both are positive)
3A = 4B

This tells us the ratio of their speeds is 4 to 3. In other words, over the same time, the faster couple will travel 4/7 of the ring road, the slower couple will travel 3/7. The difference is 120 miles. And if 1/7 is 120 miles, the whole road is 840 miles.

Friday Fun - How Long is the Ring Road around Iceland?

2008-07-18T08:00:00.000-07:00

My wife and I are taking a leisurely drive around Iceland on the Ring Road... at this point we should be a little more than half way on the East side of Iceland in Egilsstaðir. However, I thought it might be fun to give you a little topical puzzle in honor of our trip.

Q: Two couples leave Reykjavik at exactly the same time traveling opposite directions on the Ring Road around Iceland. When they meet later, one couple has traveled 120 miles farther than the other. After a night's rest in a hotel and some refueling, the couples continue their respective drives. The first couple arrives back at Reykjavik 9 hours later, the second couple takes 16 hours. Assuming that each couple maintains the same constant speed each time they drive, how long is the Ring Road around Iceland?

I'll post the answer next Friday.

How old is Mark?

2008-07-11T00:54:00.000-07:00

For everyone that struggled with the pencil puzzle, here's another algebra puzzle to "stretch your neurons". Pay attention...

The combined ages of Mark and Ann are forty-four years, and Mark is twice as old as Ann was when Mark was half as old as Ann will be when Ann is three times as old as Mark was when Mark was three times as old as Ann.

How old is Mark?

Catch That Bus!

2008-06-30T02:14:00.000-07:00

The local bus leaves Ashwood at 9:21 am and arrives in Baytree at 12:06 pm on the same day. The express bus leaves Ashwood at 10:00 am, traveling the same route, and arrives in Baytree at 11:40 am. At what time does the express bus pass the local bus if each is traveling at a constant speed?

Guess this Social Security Number

2008-06-07T15:34:00.000-07:00

A certain Social Security Number has the following qualities:

It uses each of the digits 1 to 9 exactly once (with no zero).
The digits from 1 to 2 (inclusive) add up to 12.
The digits from 2 to 3 (inclusive) add up to 23.
The digits from 3 to 4 (inclusive) add up to 34.
The digits from 4 to 5 (inclusive) add up to 45.
The digit 3 is NOT next to a dash (XXX-XX-XXXX).

What is this unique Social Security Number?

Googol to the Googol-th Power

2008-05-16T17:16:00.000-07:00

At this point everyone should be familiar with the number "googol" which is 10^¹⁰⁰ (10 to the 100th power). Written down it is a one followed by 100 zeroes.

The question this week is:

Q: How many zeroes are there in googol^^googol
(googol to the "googol-th" power)?

Mothers' Day Puzzle for all our Supermoms

2008-05-09T17:05:00.000-07:00

Take the following mathematical equation:

MOM² = AMAZON

Can you replace each letter with a different digit {0 to 9} so that the equation makes sense? The letter will represent that digit everywhere the letter appears.

U.S. Timezone Conundrum

2008-04-25T01:26:00.000-07:00

Wendy lives in a state that is on the West Coast. Edward, on the other hand, lives in a state that is on the East Coast. One day Wendy calls from her home and finds Edward also at home.

"Hey Edward, I'm not so good with timezones. I was wondering. What time is it there?"

Edward, checks his clock and reports back with the accurate time.

"That's funny," says Wendy. "It's exactly the same time here."

Where do Wendy and Edward live and how can this be?

Can you turn 2008 into 73?

2008-04-11T22:33:00.000-07:00

Okay, here's another puzzle in the 2008 series. Can you use the digits in 2008 to form an expression that will equal 73.

If you need the full instructions, check the prior puzzle which had a different target result but the same rules.

2008 Math Expression Puzzle

Hitting the Target Puzzle

2008-04-04T17:02:00.000-07:00

Here's a quick puzzle. In the attached image, a circle is inscribed in a square which is inscribed in another circle.

Of the outside yellow ring, or the inside magenta circle, which has the bigger area, and why?

Billiard Balls Puzzle

2008-03-21T17:12:00.000-07:00

In the American game of "eight-ball" there are 15 numbered balls (1 through 15). At the beginning of the game, these balls are racked into a triangular pattern as shown.

The challenge this week is to place the numbers 1 through 15 into an upside-down triangle pattern such that each number is the result of *subtracting* the two numbers above it. To eliminate mirrored answers, provide a solution where the numbers at the three points of the triangle are in ascending order going clockwise.

P.S. When taking the difference, always use the absolute value. Feel free to add a comment with your answer, along with how you solved it.

Playing with Blocks

2008-03-14T13:59:00.000-07:00

Here's a fun puzzle to ponder.

A certain number of faces of a large wooden cube are stained. Then the block is divided into equal-sized smaller cubes. Counting we find that there are exactly 45 smaller cubes that are unstained. How many faces of the big cube were originally stained?

Feel free to add a comment with your answer, along with how you solved it.

Can you turn 2008 into 97?

2008-03-07T11:09:00.000-08:00

Come on all you genius puzzlers... I'm sure you can solve the on-going challenge from last week.

In case you missed it, here is the link:
Use the digits in 2008 to form an expresion that will equal 97

A Puzzle for Leap Day, 2008 -- Can you make 97?

2008-02-29T16:29:00.000-08:00

Today is February 29, a special date that only appears on our calendars every four years. There are exceptions to this 4 year rule on century years (those ending in 00). These years are NOT leap years unless the century is evenly divisible by 400. For example, 2000 was a leap year, but 2100 will NOT be. The cycle of leap years on our calendar repeats in a 400 year cycle. Within that cycle there will be 97 leap years.

All this historical information was a way to introduce this week's math puzzle.

Q: Using each of the digits in 2008 and standard math operations, can you write an expression that equals 97?

Rules:

Each of the digits 2, 0, 0, 8 must be used. (2 and 8 will appear once, 0 will appear twice.)
You may use standard math operations of +, -, x, /, √(square root), ^(raise to a power) and !(factorial) along with parentheses for grouping.
Decimal points and multi-digit numbers may be used (e.g. 20, 208, .02 or 2.8
If squaring is done, that uses up the digit 2.
0! is agreed to have a value of 1.
Anything raised to the zero power (i.e. x^0) is 1, but 0^0 may not be used (undefined)
The integer/floor/ceiling/round functions may NOT be used.
Change of bases may NOT be used.
Logarithms may NOT be used.
Sine and Cosine may NOT be used.

Edit: The answer is now available in the comments... but don't look if you still want to figure it out on your own.

Use the digits 1 through 9 exactly once...

2008-02-22T00:42:00.000-08:00

This is a quick puzzle that shouldn't be too difficult to figure out.

Q: Arrange the digits 1 through 9 to form three 3-digit perfect squares. You must use each of the nine digits exactly once.

Feel free to add a comment with your answer, along with how you solved it.