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

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.

NPR Sunday Puzzle (Aug 3): Mathematical Synonyms

NPR Sunday Puzzle (Aug 3): Mathematical Synonyms:

Q: Start with an eight-letter mathematics term. Remove the first, fourth and eighth letters to produce a synonym of the original word. What is it?

A small percentage of the population might struggle on this, but I think most will find this puzzle relatively easy.

Edit: I was probably too obvious with the hints which included obvious synonyms of the answers. Check the comments for other hints that were provided.

A: FRACTION --> RATIO

Friday Fun - Cycling on the Bridge

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

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?

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?

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?

NPR Sunday Puzzle (Jun 29): Anyone have a Pencil?

NPR Sunday Puzzle (Jun 29): Anyone have a Pencil?:

Q: A man buys 20 pencils for 20 cents and gets three kinds of pencils in return. Some of the pencils cost 4 cents each, some are two for a penny and the rest are four for a penny. How many pencils of each type does the man get?

It's a rare NPR *math* puzzle. Using algebra you could write an equation for the number of pencils, and one for the cost of the pencils. But that results in two equations and three unknowns. Fortunately there are some constraints and a little trial and error will get you the answer. Note: You have to have at least one of each type, so just getting 4 of the first type and 16 of the last type wouldn't work.

Edit: I think the thing that confused most people was they assumed they had to buy 4 of the 1/4 cent pencils, or 2 of the 1/2 cent pencils. You can't make 20 cents with those constraints. Here's how I solved it.

Let A be the number of 4 cent pencils.
Let B be the number of 1/2 cent pencils.
Let C be the number of 1/4 cent pencils.

Number of pencils:
A + B + C = 20 pencils

Cost of pencils:
4A + B/2 + C/4 = 20 cents
Multiplying this second equation by 4 to remove the fractions we have:
16A + 2B + C = 80

Now subtract the first equation to eliminate one variable:
15A + B = 60

There are some obvious constraints on A. Because you need at least one of each type of pencil, none of the values can be 0. That eliminates A = 0 or A = 4. Trying the other values you get:
A = 1, B = 45 --> too many pencils
A = 2, B = 30 --> too many pencils
A = 3, B = 15 --> C = 2

A:
3 pencils (at 4 cents) = 12 cents
15 pencils (at 1/2 cent) = 7 1/2 cents
2 pencils (at 1/4 cent) = 1/2 cent

Catch That Bus!

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?

NPR Sunday Puzzle (Jun 8): 5-Digit Sequence

NPR Sunday Puzzle (Jun 8): 5-Digit Sequence:

Q: A calculator displays a five-digit number. The first four digits are 8735. These digits form a logical sequence. What is the fifth number in the series?

I was led down the wrong path initially because I didn't read the puzzle carefully. There's an important clue in the question which you'll see if you are bright.

Edit: The key to the puzzle was to realize that these digits were on a calculator. I mentioned that in my clue along with the additional hints of "LED", "see" and "bright". I mentioned the word "segment" in one of my comments too.

A: The next digit is also 5. Each digit is the number of LED/LCD segments that are lit in the prior digit.

Guess this Social Security Number

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

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

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

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?

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

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

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

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?

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?

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...

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.