Welcome to The Puzzler. Every week, there are 2 new puzzles related to my passion: math, logic, and thinking. The first puzzle will be The Puzzler Quik, meant for those who crave something fun-sized. The second puzzle will be The Puzzler Think, meant for those who love to ponder. The answers will be posted in next week’s column. Don’t forget to submit your answer for a potential shout-out in the next edition of the Puzzler.
Puzzler Quik
A Pizzeria lists prices for their extra toppings in pairs. Each topping costs a whole-dollar amount!
Pineapple & Hot Peppers $7
Broccoli & Extra Cheese $6
Mushrooms & Onions $2
Black Olives & Hot Peppers $5
Pepperoni & Mushrooms $4
Onions & Black Olives $3
Extra Cheese & Mushrooms $5
How many dollars do the pineapples cost?
Puzzled?
Try using variables for each ingredient.
Treat these as simultaneous equation.
Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms.
Puzzled?
Consider the numbers 
. These are our possible choices, so we know that our answer can be obtained by crossing out some of these fractions. Read the next hint to see what we should cross out!
We want to find the sum of those for which the numerator is relatively prime to 
.
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Blair from Florida was the winner of this shout-out!
8-15-17 is a Pythagorean triple, so we know this has to be a right triangle. 17 is the hypotenuse, so the area is 8(15)/2, which equals 60.
Last Week's Puzzler Think
This week’s shout out goes to Selena from New York! Kudos to her for solving the problem!
Since this triangle has a 90 degree angle, we know this is a right triangle. In a right triangle, the hypotenuse is always bigger than the 2 legs, so the measures of both the legs is the square root of 2. Applying the Pythagorean Theorem, we get $$\sqrt{\sqrt{2}^2+\sqrt{2}^2}=2.$$ Our answer is 2 unit!
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