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.

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.

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.

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.

Dungeon Doors Answer

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

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.

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 Answer

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

Hot and Cold Answer

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

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.

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.

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.

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.

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.

Ziggurat Answer

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