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?

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.