# July 2019 Brain Teaser Solution

A wooden cube that is 20 cm on each side is composed of 1 cm x 1 cm x 1 cm  cubes.
Q1: If you paint all 6 sides of the outside of the cube blue, how many cubes will have no blue paint?
With a 3 by 3 by 3 cube, there is just one cube in the middle that would have no paint.
With a 4 by 4 by 4 cube, there are 8 cubes in the center of the cube (2 x 2 x 2) with no paint.
With a 5 by 5 by 5 cube, there are 27 cubes in the center of the cube (3 x 3 x 3) with no paint.

Answer: The pattern continues so a 20 by 20 by 20 cube, there would be 18 x 18 x 18  (5832) cubes in the center of the cube with no paint.

Q2: What if the 20 x 20 x 20 cm cube is composed of 2 cm x 2 cm x 2 cm cubes?
Answer:  There would now be 1000 cubes (10 x 10 x 10), there would be 8 x 8 x 8 (512) cubes in the center of the cue with no paint.

# June 2019 Brain Puzzler Solution

Q: Using the numbers 2 3 4 5 and just the symbols + and =, make a true equation.

A: 5+4=32

# April 2019 Brain Puzzler Solution

Q: How can you add eight 4s together so that the total adds up to 500?

A: 444 + 44  + 4 + 4 + 4 = 500

# March 2019 Brain Puzzler Solution on the right side there are 3 pink and 3 blue
on the left side, there are 2 pink and 3 blue plus 5 green
Therefore the 5 green are equivalent to 1 pink.

On the bottom left, we can see that 1 pink = 2 green + 1 blue
so since 1 pink is 5 green and also 2 green + 1 blue,

5 green = 2 green + 1 blue
so 3 green = 1 blue or 1 blue = 3 green

Looking at the right hand side, we have 3 blue + 3 pink = 1/2(144)
If we replace blue and pnk in terms of green,
3 (3 green) + 3 (5 green) = 72
9 green + 15 green = 72
24 green = 72
1 green = 3
1 blue = 3 green = 3(3) = 9
1 pink = 5 green = 5(3) = 15

Thanks to https://solveme.edc.org/mobiles/

# February 2019 Brain Puzzler Solution

Q: A traffic light has a cycle through green, yellow, red, green, yellow, red, etc.
Red and green are each 30 seconds with a 3 second yellow inbetween.
What is the probability that while Amir is watching during a random 3 second interval  that the color changes?

A:
9/63 = 1/7
It is a 63 second cycle.
The light changes at t=30, t = 33 and t = 63 given three three second intervals:
[27,30] and [30, 33] and [60,63] is a total of 9 seconds out of the 63 second interval