# February 2016 Brain Teaser Solution

Some people think January 1, 2000 was the first day of the 21st century. Others think it was January 1, 2001. But everyone should agree that January 1, 2002 was the first “sum-day” of the new century- when you write out the date in numbers, 01/01/02, and 1+1=2. A sum-day is a date in which the day and month add up to the last two digits of the year. With that in mind:
A) What is the last sum-day of the 21st century?
B) How many sum-days are there in the 21st century?
A) The last sum day is 12/31/43 or December 31, 2043
B) 365 as every day in a standard (non-leap) year is part of a sum-day for some year.
For example, November 24 is a sum-day for the year 2035, because 11+24=35. But the leap day doesn’t work because February 29, 2+29=31, but 2031 will not be a leap year.

# December 2015 Brain Teaser Solution

Notice that 5 has an exclamation point on it.  This means factorial so that 5! = 5 x 4 x 3 x 2 x 1 = 120.

# November 2015 Brain Teaser Solution

Which is greater, 2^1100 or 3^700?
Bonus: Approximately how many times greater is it (to the nearest 10)?
Both of these are too large to do on a calculator and will force the calculator into overflow.  So we have to come up  with another way to compare them rather than getting both actual values.
We can write them as:
(2^11)^100   and (3^7)^100 and just compare the
2^11   vs 3^7
2048 vs 2187
so 3^700 is the winner!!
Thanks for solving

# October 2015 Brain Teaser Solution

Q: How many squares are on an 8 x 8 checkerboard?  10 x 10? How many rectangles?

8 x 8 There are:
64 1 x 1
49 2 x 2
36 3 x 3
25 4 x 4
16 5 x 5
9  6 x 6
4 7 x 7
1 8 x 8 for a total of 204 squares

For 10 x 10
100 1 x 1
81 2 x 2
64 3 x 3
49 4 x 4
36 5 x 5
25 6 x 6
16 7 x 7
9 8 x 8
4 9 x 9
1 10 x 10

for a total of 385 squares

The rectangle counting is significantly more challenging.