Logic Problems
The Holiday Cookie Mystery: Three friends—Maya, James, and Sofia—each baked a different number of cookies: 24, 36, or 48. Use the clues to figure out who baked how many:
Maya baked twice as many as someone else
James didn't bake the most
Sofia baked 12 more cookies than James
Maya: 48
James: 24
Sofia: 36
The Mysterious Age: I am thinking of a number. If you multiply it by 4, then subtract 8, you get 24. What's my number?
8
Magic Square Challenge Complete this magic square where each row, column, and diagonal adds to 15:
2 | _ | _
_ | 5 | _
_ | _ | 8
2, 7,6
9, 5, 1
4, 3, 8
The Hot Chocolate Stand: You sell hot chocolate for $3 per cup. You spent $18 on supplies. How many cups do you need to sell to break even? How much profit if you sell 25 cups?
Answer: 6 cups to break even; $75 profit
3x=15
x=5
The Gift Exchange: Four people are doing a Secret Santa. Each person bought a gift costing $12, $18, $24, or $30. Figure out who bought what:
Alex spent $12 more than Taylor
Jordan spent half of what Casey spent
Taylor didn't spend the least
Casey spent more than $20
Alex: $30
Taylor: $18
Jordan: $12
Casey: $24
The Pizza Problem: A pizza is cut into 8 equal slices. Three friends eat 2 slices each. What fraction of the pizza is left? If the whole pizza cost $24, how much is the remaining pizza worth?
$6
The Number Pyramid Each brick is the sum of the two bricks below it. Fill in the missing numbers:
__
__ __
12 __ 9
41
22 19
12 10 9
The Playlist Problem: Your holiday playlist has songs that are 3, 4, or 5 minutes long. You have exactly 12 songs totaling 47 minutes. If you have 4 songs that are 3 minutes and 5 songs that are 4 minutes, how many are 5 minutes?
3 songs (5 minutes each)
2x+5=17
x=6
The Movie Marathon: Four friends watched different holiday movies that were 90, 105, 120, and 135 minutes long. Determine the order they watched them:
-They started with a movie shorter than 2 hours
-The third movie was 15 minutes longer than the second
-The last movie wasn't the longest
-The second movie was 105 minutes
90, 105, 120, 135 minutes
The Sneaky Snowman: I'm a three-digit number. My hundreds digit is 3 times my ones digit. My tens digit is the sum of my hundreds and ones digits. The sum of all my digits is 12. What number am I?
363
Cross Number Puzzle: Create a crossword-style grid where you solve math problems to fill in answers:
Across:
144 ÷ 12 = ?
The product of 7 × 8
100 − 37 = ?
Down:
6 + 9 = ?
Half of 52 = ?
9 × 7 = ?
Across:
144 ÷ 12 = ? → 12
The product of 7 × 8 → 56
100 − 37 = ? → 63
Down:
6 + 9 = ? → 15
Half of 52 = ? → 26
9 × 7 = ? → 63
The Wrapping Paper Dilemma: A roll of wrapping paper is 24 feet long. Each gift uses 3 feet. How many gifts can you wrap? If you wrap 7 gifts, how much paper is left?
(Answer: 8 gifts; 3 feet left)
How do you make the number 7 even without addition, subtraction, multiplication, or division?
Drop the "S" and "seven" becomes "even"
Four bands played back-to-back at a local festival. Their set lengths were 30, 45, 60, and 75 minutes. Determine the order they played (first → fourth):
The 1st opened with a set shorter than 50 minutes.
The second set was 15 minutes longer than the opener.
The third set was twice as long as the opener.
The final set wasn't the shortest.
Final order (first → fourth): 30, 45, 60, 75 minutes.
The Present Puzzle: A rectangular present has a perimeter of 48 inches. Its length is twice its width. What are the dimensions?
8 inches wide; 16 inches long
The Ornament Pattern: Red, Blue, Blue, Red, Blue, Blue, Red, __, __ If this pattern continues for 30 ornaments, how many will be blue?
20
How can you write down eight eights so that they add up to one thousand?
888 + 88 + 8 + 8 + 8 = 1000
How many times can you subtract the number 5 from 25?
Once, because after you subtract 5 from 25 it becomes 20.
The Bake-Off Times
Four contestants finished baking at different times: 40, 60, 80, and 100 minutes. Determine the order they finished (1st → 4th):
The first finisher didn't take the longest.
The second finisher took 20 minutes longer than the first.
The third finisher took twice as long as the first.
The fourth finisher took 100 minutes.
40, 60, 80, 100
How can you take 2 from 5 and leave 4?
F I V E Remove the 2 letters F and E from five and you have IV which is the Roman numeral for four.
The Growing Snowman Day 1: 3 snowballs, Day 2: 6 snowballs, Day 3: 9 snowballs If this pattern continues, how many snowballs on Day 10? On what day will there be 45 snowballs?
Answer: 30 snowballs; Day 15
How many sides does a circle have?
Two. The inside and the outside.
When John was six years old he hammered a nail into his favorite tree to mark his height. Ten years later at age sixteen, John returned to see how much higher the nail was. If the tree grew by five centimeters each year, how much higher would the nail be?
The nail would be at the same height since trees grow at their tops.