Daily two puzzles for contemplation. 10 and 32

Day Ten

Difficulty: easy-ish.

Problem 32:

Difficulty: Tricky. It seems easy, but then tries to kneecap you.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 10 and answer 32.

Daily Two. 9 and 33

Day Nine.

Difficulty: easy-ish.

Number 33: 

Difficulty: Hard.
(or as the kids said, OMFG)
It's actually more complicated than hard.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 9 and answer 33.

Daily Two. 8 and 34

Day Eight will make you think a second ... or ten.

Difficulty: easy.

Difficulty: Hard-ish
(if they don't know the 3D Pythagorean theorem and have to work it out.)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 8 and answer 34.

Daily Two. 7 and 35

Problem 7

Difficulty: so easy the kids kept second-guessing themselves. ;-)

Problem 35

Difficulty: Hard (last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 7 and answer 35.

Daily Pair of Problem Puzzles. 6 and 36

Day Six will make you think a bit.

Difficulty: easy - ish.

Difficulty: Hard (last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 6 and answer 36.

Daily Problem Pairing. 5 and 37

Day Five, Number 5

Difficulty: easy.
and Problem 37 because 38 was already posted and I didn't want to lose any of the comments.

Difficulty: Hard. (Last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 5 and answer 37.

Daily Puzzle Pairing. 4 and 39

Problem (4)

Difficulty: first page.

Problem 39

Note: Remainder.
Difficulty: Hard. (last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Yeah, I know, it should read "larger" and "smaller" but I didn't have the energy to fix it.


answer 4 and answer 39.

Daily, they'll get harder. 3 and 40

Day Three

Difficulty: easy.

I'm going to save my self some time and just include the difficult one with the easy one every day.
 Please enjoy this mathematical tidbit.

Difficulty: Hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 3 and answer 40.

Daily Puzzle Pairing. 41

Since there are so many truly able mathematicians among my readers, I've decided to give them something to keep busy with! This set will start at the hardest and work backwards.

Difficulty: hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.

Daily, they'll get harder. 2

Day two.

Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.

Daily, they'll get harder. 38

Daily, they'll get harder.  How hard? Try this one:

Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

Answer is here.

Daily, they'll get harder. 1

Day one. Question 1

Difficulty: easy.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.