Tuesday, November 8, 2011

Rocket Science

Here is a new puzzle. If you think that you know the answer, please post it in the comments section.



Joe is buying model rockets from a hobby store. He is buying 6 different types of rockets, tiny, small, medium, large, huge and gargantuan. All quantities of rockets bought are positive whole numbers. He buys 2 more large rockets than medium rockets. The number of small rockets he buys is equivalent to the square root of the number of large rockets he buys. The number of tiny rockets he buys is equivalent to the number of large rockets he buys plus the number of small rockets he buys plus twice the number of medium rockets he buys. The number of huge rockets he buys is equivalent to (number of medium rockets he buys + number of tiny rockets he buys + number of small rockets he buys)0.5. The number of gargantuan rockets he buys equals the number of medium rockets he buys multiplied by the number of huge rockets he buys divided by the number of small rockets he buys minus the number of large rockets he buys. Before tax, tiny rockets cost $9.75 each, small rockets cost $12.50 each, medium rockets cost $15.25 each, large rockets cost $20.00 each, huge rockets $27.20 each and gargantuan rockets cost $36.00 each. There is a sales tax of 8% on each rocket. Joe does not buy more than 300 rockets. How much does he spend on the rockets?

Thursday, October 13, 2011

Tetra Terror

Here is a new math puzzler. If you think that you know the answer, please post it in the comments section.


Let x be a number
x=22+23+24+25+26+27+28+29+210+211+212+213+214+215
What is the value of x?

Friday, September 30, 2011

Perdido na tradução

In this post is the new math puzzle. If you think that you know the answer, please post it in the comments section. In honor of today being Agricultural Reform Day in Sao Tome and Principe and International Translation Day, parts of this puzzler are written in Portuguese (These parts are underlined).


Joe e Jane estão jogando um jogo chamado duelo cartão. Neste jogo, dois baralhos completos (sem jokers) são embaralhados juntos. The two players then take turns drawing cards off the top of the deck, one at a time. Whoever gets two of the same card first (suit and rank) wins. If Joe goes first, what is his percent chance of winning? Por favor, volta a sua resposta com a aproximação de décimo de milésimo de um por cento.

Thursday, September 15, 2011

Eight Bones

Here is todays Puzzler. If you think that you know the answer, please post it in the comments section. This is the final puzzle in the summer competition. It is worth 2 points.

If eight six sided dice are rolled, what is the probability that no two dice will add up to seven? Please give your answer as a percentage and round to the nearest hundredth of a percent.

Tuesday, June 28, 2011

Gems of Sumia

Here is todays puzzle. If you think that you know the answer, please post it in the comments section. This puzzle is worth 4 points in the summer competition.

The King of Sumia has 23 gems. Each of these gems has a number, All of the gems are prisms that have bases that are regular polygons. Each gem has its own box. The boxes all have letters on them, A-W. The gem with the greatest volume goes in box A, the one with the next greatest volume goes in box B, and so on. Below is a list of how many sides are on each gems base, how long each side is and how tall each gem is.
Gem 1: 3 sides, 13 side length, 22 height
Gem 2: 4 sides, 15 side length, 8 height
Gem 3: 5 sides, 11 side length, 10 height
Gem 4: 6 sides, 7 side length, 15 height
Gem 5: 7 sides, 14 side length, 15 height
Gem 6: 8 sides, 6 side length, 19 height
Gem 7: 9 sides, 8 side length, 15 height
Gem 8: 10 sides, 8 side length, 9 height
Gem 9: 11 sides, 7 side length, 18 height
Gem 10: 12 sides, 6 side length, 15 height
Gem 11: 13 sides, 6 side length, 13 height
Gem 12: 14 sides, 6 side length, 9 height
Gem 13: 15 sides, 9 side length, 11 height
Gem 14: 16 sides, 5 side length, 4 height
Gem 15: 17 sides, 3 side length, 10 height
Gem 16: 18 sides, 6 side length, 6 height
Gem 17: 19 sides, 5 side length, 10 height
Gem 18: 20 sides, 3 side length, 6 height
Gem 19: 21 sides, 4 side length, 3 height
Gem 20: 22 sides, 2 side length, 3 height
Gem 21: 23 sides, 3 side length, 2 height
Gem 22: 24 sides, 3 side length, 6 height
Gem 23: 25 sides, 2 side length, 4 height
Which gem goes in each box?

The answer will be posted on Monday or when somebody posts an answer in the comments section.

Monday, June 13, 2011

Fun with Factors

Here is todays puzzle. If you think that you know the answer, please post it in the comments section. This puzzle is worth 3 points in the Summer Competition.

What is the sum of the non-semiprime numbers on the list below minus the number on the list below that has the most distinct prime factors?

36064, 14101, 60303, 99362, 11287, 97462, 73941, 92428, 65799, 53422, 13276, 37968, 45785, 37112, 50485, 51963, 29444, 41506, 16199, 60497, 57592, 91774, 63447, 43749.

The answer will be posted when somebody posts an answer.

Sunday, June 12, 2011

Der Sequenz Wieder Answer

Contained within this post is the answer to the puzzle posted on June 6th. One answer was posted. If the answer is correct, the poster gets 3 points. If not, the points go unclaimed. The answer is after the jump.

Friday, June 10, 2011

Package Stackage

Here is todays puzzle. If you think that you know the answer, please post your guess in the comments section. This puzzle is worth 2 points in the Summer Competition.

At the Cremliville Post Office, there are 2 stacks of rectangular packages with square bases. Stack A has 18 packages. The bottom one is 18 inches long and 1 inch high. Each package in stack A is 1 inch less in length and 2 inches more in height than the one below it. Stack B has 22 packages. The bottom one is 22 inches long and 1 inch high. Each package in stack B is 1 inch less in length and 1 inches more in height than the one below it. Which stack has the larger average package size and what percent greater is the larger average package size than the smaller average package size? Please round your answer to the nearest hundredth of a percent.

The answer will be posted when an answer is posted in the comments section.

Wednesday, June 8, 2011

Omnicheese Answer

Contained within this post is the answer to the puzzle posted on June 2nd. One answer was posted. If it is correct, the poster scores 3 points. If not, the points go unclaimed. The answer is after the jump.

Monday, June 6, 2011

Der Sequenz Wieder

Here is todays puzzle. If you think that you know the answer, please post it in the comments section. This puzzle is worth 3 points in the Summer Competition.

What are the next 3 terms in the following sequence?
210, 1155, 5005, 17017, 46189, 96577 ...

The answer will be posted on Friday or when a guess is posted in the comments section.

Triangles, not Hexagons Answer

Contained within this post is the answer to the puzzle posted on May 31st. One person posted an answer. If his answer is right, he scores 2 points. If the answer is wrong, the points go unclaimed. The answer is after the jump.

Thursday, June 2, 2011

Omnicheese

Here is todays puzzle. If you think that you know the answer, please post it in the comments section. This puzzle is worth 3 points in the Summer Competition.

Omnimart is having another sale. Discounts are avalible on American, Swiss and Limburger cheese, peanuts and chocolate milk. The discount on Limburger cheese is (blocks of Swiss cheese bought*4)%. The discount on Swiss cheese is (blocks of American cheese bought*3)%. The discount on American cheese is (blocks of Limburger cheese bought*3.5)%. The discount on peanuts is (blocks of cheese bought)%. The discount on chocolate milk is (blocks of American cheese bought*blocks of Swiss cheese bought*blocks of Limburger cheese bought*cans of peanuts bought/1000)$. The prices of the products are listed below.
Block of American cheese: 3.00$
Block of Swiss cheese: 4.00$
Block of Limburger Cheese: 5.00$
Can of peanuts: 1.50$
Gallon of chocolate milk: 3.00$
You are on a budget of 80$. If you buy 7 blocks of American cheese, 5 blocks of Swiss cheese, 10 cans of peanuts and 3 gallons of chocolate milk, how many blocks of Limburger cheese can you buy? You can't buy a partial block of Limburger cheese.

The answer will be posted on Wednesday.

Blokies Answer

Contained within this post is the answer to the puzzle posted on May 27th. The answer is after the jump.

Tuesday, May 31, 2011

Triangles, not Hexagons

Here is todays puzzle. If you think that you know the answer please post it in the comments section. This puzzle is worth 2 points in the summer competition.

What is the sum of the first 66 triangular numbers that are not hexagonal and not divisible by 3?

The answer will be posted Monday.

Casual Math Puzzlers Summer Competition

Prepare for an amazing battle of mathematics! The Casual Math Puzzlers Summer Competition has begun! Throughout the summer, the first person to post the correct answer to a puzzle in the comments section will earn points in the competition. The number of points awarded will be determined by the difficulty of the puzzle. At the end of the competition in early September, the person with the most points will win glory, bragging rights and a spot on the soon to be existent Page of Fame. The first puzzle in the competition will be posted later today. Good luck.

Metasphere Answer

Contained within this post is the answer to the puzzle posted on May 25th. The answer is after the jump.

Friday, May 27, 2011

Blokies

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

Blokies are a small, block like creature. Blokies are either orange or green. All blokies have a number on their back. Every hour, a blokie spawn happens. If the number of blokies the same color as a blokie is less than or equal to the number on that blokie, that blokie spawns a new blokie. The number on a new blokie depends on the blokie spawning it. If the spawner is orange and has an odd number on it, the number on the new blokie is three times the number on the spawner minus 1. If the spawner is orange and has an even number on it, the number on the new blokie is two times the number on the spawner minus 1. If the spawner is green and has an odd number on it, the number on the new blokie is three times the number on the spawner plus 1. If the spawner is green and has an even number on it, the number on the new blokie is two times the number on the spawner plus 1. There is an orange blokie and a green blokie, each with the number 1 on them. After 9 spawns, what will be the value of (sum of the numbers on green blokies)/(sum of numbers on orange blokies)? Please give your answer rounded to the nearest humdredth.

The answer will be posted on Thursday.

Schrodinger's M&Ms Answer

Contained within this post is the answer to the puzzle posted on May 24th. The answer is after the jump.

Wednesday, May 25, 2011

Metasphere

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

Alfred has a metasphere. The metasphere is made of a blue material and a red material. At the center of the metasphere is a sphere of blue material that has a diameter of 1mm. That sphere is covered by a 1mm thick layer of red material. Then that sphere is covered by a 2mm thick layer of blue material. The layers keep increasing in thickness, with each layer being the thickness of the past 2 layers combined. There are 12 layers. The layers alternate red and blue materials. The blue material has a density of 1.7 grams/cubic centimeter. The red material has a density of 2.7 grams/cubic centimeter. What is the mass of the sphere? Please give your answer in grams and round to the nearest hundredth.

The answer will be posted on Tuesday.

Riddle of the Sphenics Answer

Contained within this post is the answer to the puzzle posted on May 20th. The answer is after the jump.

Tuesday, May 24, 2011

Schrodinger's M&Ms

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

There is a closed box with 34 M&Ms inside of it. 15 of the M&Ms are green, 12 are yellow and 7 are red. When the box is opened, the M&Ms either change color or cease to exist. Each green M&M has a 1/2 chance of becoming yellow, a 1/4 chance of becoming red and a 1/4 chance of ceasing to exist. Each yellow M&M has a 3/5 chance of becoming red, a 1/5 chance of becoming green and a 1/5 chance of becoming non existent. Each red M&M has a 13/25 chance of becoming green, a 6/25 chance of becoming yellow and a 6/25 chance of ceasing to exist. What is the expected color distribution of the M&Ms after opening the box?

The answer will be posted on Friday.

Monday, May 23, 2011

Dungeon Doors Answer

Contained within this post is the answer to the puzzle posted on May 17th. The answer is after the jump.

Friday, May 20, 2011

Riddle of the Sphenics

Happy World Metrology Day! Today is a celebration of the signing of the Metre Convention in 1875. The Metre Convention established three international organizations to oversee the keeping of metric standards. It also has absolutely nothing to do with todays puzzle. If you think that you know the answer, please post it in the comments section.

A sphenic number is a positive integer that is the product of three distinct prime numbers. A pronic number is a number that is the product of 2 consecutive non-negative integers. What is the product of the average value of the first 20 sphenic numbers and the average value of the first 20 pronic numbers?

The answer will be posted on Wednesday.

The Return of the Poker Chips Answer

Contained within this post is the answer to the puzzle posted on May 16th. The answer is after the jump.

Tuesday, May 17, 2011

Dungeon Doors

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

Guido has been thrown into a dungeon. There are 3 doors in the dungeon. The first one is 4 feet wide, 3 feet long, 3 inches thick and has a density of 8746 kg/cubic meter. The second door is 41 inches wide, 41 inches long, 3 inches thick and has a density of 8800 kg/cubic meter. The third door is 5 feet wide, 5 feet long, 1.5 inches thick and has a density of 8470 kg/cubic meter. All three doors have passages behind them. The passage behind the heaviest door leads to freedom. The other two lead to a hungry dragon. Guido does not want to become the dragons lunch. Which door should he choose.

The answer will be posted on monday.

Monday, May 16, 2011

The Return of the Poker Chips

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

There are 3 red poker chips , 2 yellow poker chips and 1 blue poker chip in a bag. A poker chip is chosen out of the bag at random. That chip is discarded and 1 new poker chip of each color is put back into the bag. After this process is done three times, the number of chips in the bag of each color are counted. Red chips are worth 3 dollars each, yellow chips are worth 2 dollars each and blue chips are worth 1 dollar each. What is the most likely value of the chips in the bag?

Crashing Cars Answer

Contained within this post is the answer to the puzzle posted on May 11th. The answer is after the jump.

Friday, May 13, 2011

Hot and Cold Answer

Contained within this post is the answer to the puzzle posted on May 9th. The answer is after the jump.

Wednesday, May 11, 2011

Crashing Cars

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

There is a blue car driving east at 35 miles per hour. Directly east of the blue car is a red car driving west at 45 miles per hour. the front bumpers of the two cars are a half of a mile apart. In between those cars is a silver car that is 14 feet 8 inches long and is driving east. The back bumper of the silver car is 500 feet away from the front bumper of the blue car. How fast does the silver car have to be going for the blue car and the red car to hit it at the same time? Please give your answer in miles per hour and round to the nearest one hundredth.

Combination Lock Answer

Contained within this post is the answer to the puzzle posted on May 6th. This was a very difficult puzzle. The answer is after the jump.

Monday, May 9, 2011

Hot and Cold

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

In Antarctica, a scientist observes that the outside temperature is -93 degrees Fahrenheit. In Ithaca, there is an oven that is twice as hot as the location in Antarctica. What is the temperature of that oven in degrees Celsius?

The answer will be posted on Friday.

The Roots Answer

Contained within this post is the answer to the puzzle posted on May 4th. The answer is after the jump.

Friday, May 6, 2011

Combination Lock

Here is todays puzzle. If you think you know the answer, please post it in the comments section.

You are trying to figure out the combination to a lock. The combination contains 3 numbers between 1 and 50. To help you, you have these four hints.
1. The product of the three numbers is 13860
2. Only the first 2 numbers are divisible by three
3. Only the last 2 numbers are divisible by two
4. The second number is the largest number

The answer will be posted Wednesday.

Cyclic Baseball Answer

Contained inside this post is the answer to the problem posted on May 3rd. The answer is after the jump.

Wednesday, May 4, 2011

The Roots

Here is todays puzzle. If you think you know the answer, please post your guess in the comments section.

Which of the following base 8 numbers, when converted to base 10, has the lowest digital root?

23730
12533
76722
16411
21641
55564
11225
125055
22353
1744
74617
16231

The answer will be posted on monday.

Triangle 161 Answer

This post contains the answer to the puzzle posted on April 28th. The answer is after the jump.


Tuesday, May 3, 2011

Cyclic Baseball

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

In baseball, hitting for the cycle means that a player hits a single, a double, a triple and a home run all in one game. At any given at bat, Jim has a 17.5% chance of hitting a single, a 6% chance of hitting a double, a 1.5% chance of hitting a triple and a 2.5% chance of hitting a home run. What is the chance of Jim hitting for the cycle in a game where he has 4 at-bats? Please give your answer as a percent.

The answer will be posted on Friday.

Monday, May 2, 2011

Ziggurat Answer

This post contains the answer to the problem posted on April 26th. The answer is after the jump.

Thursday, April 28, 2011

Triangle 161

Here is todays math puzzle. If you think you know the answer, please post it in the comments section.

What is the perimeter of the largest right triangle with all integer side lengths, one of which has a length of 161?

A Magic Sphere Answer

We had three people post their guesses to the problem that was posted on April 22nd. One guess was correct. The answer is after the jump.

Tuesday, April 26, 2011

Ziggurat

Here is a new puzzle. If you think you know the answer, please post it in the comments section.

The Sumians are building a ziggurat. They are building it out of blue and red cubes with a volume of one cubic meter. The ziggurat will be built in 32 layers that are centered on top of each other. From the top, the number of stones in the layers will go 1, 4, 9, 16, 25... All layers will be square. All stones that are visible on the outside are going to be blue and all stones that are not visible from the outside are going to be red. Red cubes weigh 2100 Kilograms each and blue cubes weigh 2700 Kilograms each. What percentage of the ziggurats mass is in the blue cubes? Round your answer to the nearest tenth of a percent.

The answer will be posted on monday.

Omnimart Answer

Here is the answer to the question posted on April 21st. If you want to see the answer, please highlight between the periods.

. You buy up to 10.2 pounds of bananas without going over budget.

Please post any feedback in the comments section.

Friday, April 22, 2011

A Magic Sphere

Here is a new puzzler. If you think you know the answer, please post your guess in the comments section.

Jim has a magic sphere. Every minute, the spheres radius grows by 4%. If the sphere has a radius of 5 centimeters at noon, what is its volume at 1:30 PM?

Gridball Answer

Here is the answer to the problem posted on 4/15. If you want to see it, please highlight between the periods.

. The second throw landed in the trapezoid, the third throw landed in the square, the seventh throw landed in the chevron and the ninth throw landed in the pentagon and on a side of the trapezoid. None of the other throws landed in a shape. Marci's final score was 23.

Please post any feedback in the comments section.

Thursday, April 21, 2011

Omnimart

Here is today's puzzle. If you think you know the answer, please post it in the comments section.

The Omnimart is having a sale. If you buy toilet paper and bananas, you get a discount equivalent to $(rolls of toilet paper bought/4*pounds of bananas bought/20) on baked goods. If the discount is higher than the amount spent on baked goods, no discount is given. 6 rolls of toilet paper cost $3, a pound of bananas costs $1.25, a gallon of ice cream costs $3.50 and a bagel costs $0.65. If you are on a budget of $50 and you buy 18 rolls of toilet paper, 5 gallons of ice cream and 20 bagels, how many pounds of bananas can you buy without going over budget?

Wednesday, April 20, 2011

Zenzizenzizenzic Fantastic Answer

Here is the answer to the puzzle posted 4/13/11. Highlight the area between the periods to see the answer.

. The zenzizenzizenzic form of a number is the number to its 8th power. the first number with the letter c in it is one octillion. the zenzizenzizenzic form of one octillion is 10 to the 216th power.

Please post any feedback in the comments section.

Friday, April 15, 2011

Gridball

Here is todays puzzle. If you think you know the answer, please post it in the comments section.

Marci is playing a game called gridball. She throws a ball onto a grid with four shapes on it. If the ball lands in a shape or on one of the sides of a shape, she scores points equivalent to how many sides the shape the ball lands in has. If the ball lands in an overlap of two shapes or more, she scores points for all shapes the ball lands in. After each throw, shapes with 4 sides rotate 90 degrees counterclockwise around the origin, shapes with 5 sides rotate 180 degrees around the origin and shapes with 6 sides rotate 90 degrees clockwise around the origin. The shapes and the locations of their corners at the beginning are listed below.
Trapezoid: (-5, 4) (-1, 3) (1, -1) (-1, -4)
Square: (0, -1) (0, -7) (6, -7) (6, -1)
Pentagon: (-6, 0) (-2, -1) (2, -5) (1, -9) (-4, -6)
Chevron: (-2, 2) (1, 5) (5, 4) (6, 0) (3, -3) (2, 1)
Here are where her throws land:
1st (-4.8, -3.8)
2nd (0.6, -1.7)
3rd (-5.7, 3)
4th (5.7, 8.5)
5th (-6.1, -8.7)
6th (6.1, 7.4)
7th (-1.1, -1.5)
8th (5.8, -2.3)
9th (-2.5, -1)
10th (6.9, -0.2)
How many points does she score?


Number Sequence Answer

Below is the answer to the problem posted April 8th. If you want to see the answer, please highlight between the periods.
. The next three numbers are 364, 596 and 972. If you take the difference between the numbers in this sequence, you get a sequence that goes 1, 2, 4, 7, 12, 20, 33... If you take the differences between the terms in that sequence, you get the Fibonacci sequence.

Please post any feedback in the comments section.

Wednesday, April 13, 2011

Zenzizenzizenzic Fantastic

Here is todays puzzle. If you think you know the answer, please post your guess in the comments section.

Zenzizenzizenzic contains the most z's of any word in the English language. What is the zenzizenzizenzic form of the first number that when spelled out contains the letter c?

Guess the Number Answer

Here is the answer to the problem posted on April 7th. If you want to see it, please highlight between the periods.

. 2916 is the product of 4, 9 and 81 and is the answer.

Please post any feedback in the comments section.

Monday, April 11, 2011

Number Sequence

This is another puzzle. If you think you know the answer, please post it in the comments section. Good luck.

What are the next three numbers in this sequence?
1, 3, 7, 14, 26, 46, 79, 133, 221 ...

First Puzzle Answer

Below is the answer to the First Puzzle. If you want to see it, highlight it.

The two probabilities are the same. Both have a one in eight chance of happening.

Please post any feedback in the comments section.

Thursday, April 7, 2011

Guess the number

In this puzzle, you will have to guess a number based on the three clues below. If you think you know the answer, please post it in the comments section.

1. The number is four digits.
2. The number is the product of 3 different square numbers.
3. The digit in the hundreds place is also the sum of the other 3 digits.

Good Luck!

Tuesday, April 5, 2011

First Puzzle

This is the first puzzle on the Casual Math Puzzlers blog. If you have a guess at the answer, please post it in the comments section.
There are two poker chips in a bag, one red and one blue. A chip is pulled out of the bag at random, then put back in the bag along with another one of the same color. After this is done seven times, is it more likely that there will be exactly five blue chips in the bag, eight red chips in the bag or are their probabilities the same?

Welcome!

Welcome to the Casual Math Puzzlers blog. Here you will find many math puzzles. New puzzles will be posted 2 or 3 times a week. Answers will be posted 3 days to a week after the puzzle. Now enjoy some math puzzles.