1. On Monday, Phil ate half a pizza. On Tuesday, he ate half the remainder. On Wednesday, he ate half the remainder. On Thursday, he ate half the remainder. After eating pizza on Thursday, what fraction of the original pizza did Phil have left? +

2. Weekly Puzzler 2 Replace each variable in a/b + c/d + e/f with a digit from 1 to 8, using each digit once, so that it has the smallest possible value.

3. Weekly Puzzler 3  A man has lived one fourth of his life in Topeka, one fifth in Sacramento, one third in Houston, and for the last 13 years, he has lived in Hartford. He has lived in no other cities. How old is the man?

4. Weekly Puzzler 4  Alec and Patrice hiked up a mountain trail at a rate of 1.5 miles per hour and descended back down the same trail at a rate of 4 miles per hour. Their hike took 6 hours. How long was the trail to the top of the mountain?

5. Weekly Puzzler 5  Celia, Darryl, and Emilie ate an entire pie. Darryl ate twice as much as Celia and Emilie ate three times as much as Celia. What fraction of the pie did Celia eat?

6. Weekly Puzzler 6 Travis cashed a check but did not notice that the cashier gave him dollars for cents and cents for dollars. Pocketing his cash, Travis dropped a nickel. When he got home, Travis counted his money and found he had exactly twice the amount of the check. What was the amount of the check?

7. Weekly Puzzler 7 Rosita spent half her cash at a sale. The number of cents in the amount she had left after the purchase equaled the number of dollars she had before the purchase. The number of dollars she had after the purchase equaled half the number of cents in the amount she had before the purchase. How much cash did she take to the sale?

8. Weekly Puzzler 8 Name a set of numbers that have the same mean, median and mode.

9. Luba needs to measure 4 ounces of chocolate for a recipe but can find only 5 and 9 ounce weights for her balance scale. How can she measure the chocolate?

10. Weekly Puzzler 10 Find x if = 4

11. Weekly Puzzler 11 If 3 pistachios and 1 walnut weigh the same as 10 peanuts, and 1 pistachio and 6 peanuts weight the same as 1 walnut, how many peanuts weigh the same as 1 walnut?

12. Weekly Puzzler 12 Li-Shyung has a pocket full of coins, with quarters the largest denomination, but she cannot give you correct change for a dollar. What is the greatest possible value of the coins in her pocket ?

13. Weekly Puzzler 13 If you write all the multiples of 7 from 7 to 98, which nonzero digit(s) do you write least often?

14. Weekly Puzzler 14 Replace each ? with +, -, *, or  to make the sentence true. (5 ? 5) ? (5 ? 5) ? 5 = 55

15. What value(s) of n make(s) the statement n = n + n true?

16. Weekly Puzzler 16 What is 2 ? What is (2 ) ? What is ((2 ) ) ?

17. Weekly Puzzler 17 Use all the digits 1, 2, 3, and 4 only once each to write three expressions that have a value of 5.

18. Weekly Puzzler 18 You are forming a rectangular landing outside your door using 2 inch by 6 inch bricks. The landing is to be 16 inches wide and 27 inches long. How many bricks would it take to fill the area? Can you fit the bricks into the rectangle without cutting any? If so, Draw a diagram.

19. Weekly Puzzler 19 Alexis, Ben, Clay, and Deb are each buying one souvenir T-shirt. They buy an X-large, a large, a medium, and a small. Alexis’ shirt is not an X-large or a medium. Ben bought either the large or the medium. Deb’s shirt is smaller than Alexis’ or Ben’s. Who bought which size?

20. Weekly Puzzler 20 Which of the numbers from -10 to 10 is the greatest distance on the number line from its absolute value? What is that distance?

21. Find two integers so that the absolute value of their sum is 6 and the sum of their absolute values is 20.

22. Weekly Puzzler 22 1 + 2 = ? 1 + 2 – 3 + 4 = ? 1 + 2 – 3 + 4 – 5 + 6 = ? 1 + 2 – 3 + 4 - … - 49 + 50 = ?

23. Weekly Puzzler 23 Find the value of x if 5 * (-2) * x * (-3) = 0

24. Weekly Puzzler 24 What is ?

25. Weekly Puzzler 25 Using the commutative and associative properties, how can you find the sum 1 + 2 + 3 + … + 100 without adding all the numbers?

26. Weekly Puzzler 26 If you know that a zip times a zap is a zowie, a zip times a zot is a zing, and half the difference of a zing and a zowie is zoop, what it’s the product of a zip and the difference of a zot and zap?

27. Find the y-coordinate of any point with the x-coordinate - 4 that is the same distance from both axes.

28. Weekly Puzzler 28 What is the least positive odd number that is not prime?

29. Weekly Puzzler 29 If a number p is prime, write an expression with p that describes the sum of all the factors of p.

30. Weekly Puzzler 30 The word form for the integer x has x letters. What is x?

31. Weekly Puzzler 31 The LCM (Least Common Multiple) of three consecutive single digit positive integers is 168. What are the integers?

32. Weekly Puzzler 32 If a 2 and b > 0, which is greater: a or b ?

33. What is (2 ) ?

34. Weekly Puzzler 34 Imagine taking a sheet of paper and folding it in half. This step is called F1. Fold the sheet in half again. This step is F2. After step F7, how many layers of paper will you have?