October 2014 Brain Teaser Solution

Q: Can you transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word?


A:THINK

Replacing N with C
THICK

Replacing H with R
TRICK

Replacing I with A
TRACK

Replacing K with T
TRACT

Replacing C with I
TRAIT

Replacing T with N
TRAIN

Replacing T with B
BRAIN

September 2014 Brain Teaser Solution

Q: I traveled home in an old car that was leaking gas and could only be driven at a steady 30 miles per hour while getting gas mileage of 20 miles per gallon.   At the start of the trip, there were exactly 10 gallons of fuel but the fuel tank lost fuel at the rate of half a gallon per hour.   Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.  How far did I drive?

A: 150 miles

Solution: 30 mph with 20 miles per gallon means that 20 miles would use 1 gallon so 30 miles uses 1.5 gallons/hour and we must also include the 1/2 gallon an hour due to the leak. 

So the gas level is decreasing by a rate of 2 gallons per hour which means that the 10 gallons will last for 5 hours.

5 hours at the steady 30 mph = 150 miles

August 2014 Brain Teaser Solution

Q:

What is the next number in this series?

1, 11, 21, 1211, 111221, 312211 

 

A: 13112221 
as the last number listed above is 312211
one 3 one 1 two 2 two 1 

1, 11, 21, 1211 , 111221, 312211, 13112221, ...

The pattern is that the next term comes from counting how many of each numbers are in the previous term. For example, the second term is 11 because there is ONE "1" in the previous term. The third term, likewise, is 21 because there are TWO "1" in the previous term. Next term is ONE "2", ONE "1", and then ONE "1", ONE "2", TWO "1", and so on and so forth.

 

July 2014 Brain Teaser Solution

Q: 8, 5, 4, 9, 1, 7, 6, 10, 3, 2, 0...what is special about this sequence?

     Where would 11 fit into this sequence?

A: The numbers are arranged alphabetically so 11 would fit in between 8 and 5

Add Placement Test Examples: Comment to Higher Ed for Higher Standards

It is wonderful to see attention on this important national issue
It would be great to have samples of the placement tests on your web site:
http://media.collegeboard.com/digitalServices/pdf/accuplacer/accuplacer-sample-questions-for-students.pdf
http://www.act.org/compass/sample/index.html
These contain the content that students need to know especially at the community college level.
Please consider adding links on your web site to these important documents  so that stakeholders can familiarize themselves with the content.  Access to these examples could benefit students, teachers, parents and society at large.
Respectfully submitted,
Robin Schwartz
Founder www.mathconfidence.com
Adjunct Prof, College of Mt St Vincent

June 2014 Brain Teaser Solution

Q: Gauss said: "The cube and the fourth power of my age contain each digit from 0 to 9 exactly once."  The professor said: "It's a good coincidence because the square and the cube of my age contain each digit from 0 to 9 exactly once."  Find their ages.

A: 18 and 69
Looking at the last digit can give us many clues in Math solutions  and BC (before calculators) was how Math was often done!
In this case, we do not want to repeat a digit in both the cube and the fourth power because all the digits have to be different.
Here is a list of perfect cubes and perfect fourths from 1 to 10
Check out how the last digits are the same for 0 1 5 6
                 Cube                   To the fourth
1                  1                                 1
2                  8                               16
3                27                               81
4                64                             256
5              125                             625
6              216                           1296
7              343                           2401
8              512                           4096
9              729                           6561
10          1000                         10000

Their ages can't end with 0, 1, 5 or 6.  

See this spreadsheet: https://docs.google.com/spreadsheets/d/1rEkYk8uShyQ8gPfwTC4Losp-RPzNIYgvMo2nu0NMV4M/edit?usp=sharing

Gauss's age is easy. Since 17^3=4913, 17^4=83521, 22^3=10648, 22^4=234256, Gauss's age is between 18 and 21. The only possibility is 18. 18^3=5832, 18^4=104976.

The professor's age is a little harder. It can be 47 to 99, and the possibilities are: 48, 53, 54, 57, 62, 63, 69, 72, 78, 84, 87, 89, 93, 98, 99. By trial and error, 69 satisfies this condition: 69^2=4761, 69^3=328509.

Therefore, Gauss was 18 and the professor was 69.

 

May 2014 Brain Teaser Solution

Q: What is the largest number possible using only three digits?  

A:   9 to the 9th to the 9th9^9 does not equal 81. 
9^9=387420489 
387420489^9=?  a big number!!!!!!

April 2014 Brain Teaser Solution

Q: Find the two numbers whose digit sum is half of the number itself.

A: 0 and 18

March 2014 Brain Teaser Solution

Q: Find the two right triangles (with whole number sides) whose perimeter and area are 24.

Meant to ask 

Find the two right triangles (with whole number sides) whose perimeter and area are the same.

A: 6 8 10 and 5 12 13

February 2014 Brain Teaser Solution

Q; Jack and Jill  have two children and one of the children is a boy. Assuming that the probability of each gender is 50/50.  What is the probability that the other child is also a boy? 

A: 1/3

The following are possible combinations of two children:

Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl

Out of the above options 3 contain at least one boy and only one of them has two boys.  So once you know that one of them is a boy, you can just focus on these 3 possible outcomes and since only one of the outcomes has two boys, the probability would be 1 out of 3 or 1/3

The Pleasures of Teaching to the Test: SAT and ACT

SAT tutoring is teaching to the test as the College Board book has old tests in it! as does the ACT.

I wish the Common Core testing would be as straightforward...Grades 3- 8 Math and ELA have samples of last year's test (but not the whole test).  Grades 3-8 Sample Questions
Spoiler alert: The answers are on the same page as the questions

Here is an article from the Wall Street Journal that shares my view that if kids know what is on the test, it can make them smarter and help us to focus on what are important skills and knowledge.

January 2014 Brain Teaser Solution

Q: Can you circle exactly four of these numbers such that the total is twelve?

1 6 1

6 1 6

1 6 1

6 1 6

A: This brain teaser is about perspective as if you turn the page (ahem, ipad, tablet, PC screen) upside down the 6 will become a 9 and then it will be easy ;)

Positive Spin on Academics Please!!! SAT is an Opportunity

To the Editor:

We need good PR in Education and even more so in Math Education.  The front page article with "The Loser Has to Do Math" could be retitled "Loser Gets to Learn Math and Loves the Challenge" to inspire people to learn rather than normalize negative feelings about Math.

We, as a nation, can raise our SAT scores along with knowledge, skills and attitude by developing a positive outlook on testing.  This could prepare students for college and greatly reduce remediation while helping people realize that studying improves one's mind just as marathon training boosts fitness. 

A 2009 WSJ article on the SAT inspired me to retake the exam but it also had a glum view of testing with the phrase "the terrifying experience of the SAT" (http://online.barrons.com/article/SB124337711110856009.html).   I prepared by doing actual old exams from the College Board book and was able to raise my old 1980 verbal score by over 200 points.  This did away with 3 decades of thinking "I am just a Math person" and furthered my belief in the power of self-improvement and the ability to influence one's own future.  

Please consider how the Wall Street Journal which often publishes caring and insightful pieces on education can help students, parents, teachers and society view test taking as an opportunity rather than a threat.

Sincerely,

Robin A. Schwartz

Founder www.mathconfidence.com

Bronx NY

In reference to http://online.wsj.com/news/articles/SB10001424052702304887104579302523403171080