# September 2017 Brain Puzzler Solution

Q; For what value of n does 3^1998 + 9^999 + 27^n = 3^1999?
(^ = to the power of)
A: 666
Rewriting each number in base 3:
3^1998 + (3^2)^999 + (3^3)^n = 3^1999
3^1998 + 3^1998 + 3^(3n) = 3^1999

It takes 3 3^1998s to make 3^1999 as 3 x 3^1998 = 3^1999
Therefore 3^(3n) = 3^1998
so 3n = 1998 and n = 666

# August 2017 Brain Teaser Solution

Q: With one straight cut a cake can be sliced into two pieces. A second cut that crosses the first one will make four pieces, and a third cut can produce as many as seven pieces. What is the largest number of pieces that you can get with six straight cuts?

A: 22
With 0 cuts, you get 1 big cake
With 1 cut, 2 pieces
With 2 cuts, 4 pieces
For the 3rd cut, if you cut cleverly you can get 7 pieces
http://bit.ly/CuttingthePieGardner

# Get the Math and Points Jun 2017 CC Alg I Regents #9

Definition of a function:
Every x maps to a unique y
Notice Jan has 31 days and that’s it
March has 31 days and April has 30 days
But the number of days in February depends on leap year vs non leap year
So which month maps to two outputs?
(https://www.timeanddate.com/calendar/months/

# Get the Math and Points June 2017 CC Alg I Regents #8

Using substitution, we can rewrite the second equation as
3(-2x + 2x + 8) = 12
3(8) = 12
24 = 12
huh?  NO solution

If we were to solve the second equation for Y=, we would get:
by distributing the 3
-6x + 3y = 12
3y = 6x + 12
Divide both sides by 3
y = 2x + 4 this is parallel to the first line y = 2x + 8 and therefore the lines will never meet

# Get the Math and Points June 2017 CC Alg I #7

First look at the graph — looks super nonlinear and pretty exponential
Use the point (0,4).
We can eliminate answers (2) and (3), as if we substitute h=0,  the output would be 6/5 and 4.2 as opposed to the 4 for the y value we are looking for.
Now we can use the point (1,8) to see if y = 8 when x = 1
For answer (4), if we substitute in x = 1, we get 2/3(1)^3 – 1^2 + 3(1) + 4 = 2/3 – 1 + 3 + 4≠ 8
Try answer (1): using order of operations: 4(2)^1 = 4(2) = 8
4(2)^2 = 16 and 4(2)^3 = 32.  That’s it –2 points
You can also use Y= and check the table for a match: