Mathematical Puzzles

Here, in this activity get ready for a thrilling challenge that will put your problem-solving skills to the test. Get ready to sharpen your minds and embrace the world of logic puzzles!

They are a series of intriguing puzzles that will challenge your ability to think critically, deduce patterns, and unlock solutions. Whether you're a seasoned puzzle enthusiast or new to the world of logic games, this segment promises to be both fun and intellectually stimulating.

So, grab a pen and paper or simply engage your mind as we embark on this journey together. By the end of this activity, you'll have exercised your logical thinking and might even discover new strategies for tackling complex problems.

Are you ready? Get started.

Riddle 1: The Missing Number

What number comes next in this sequence? 1, 1, 2, 3, 5, 8, 13, _
Hint: This sequence is known as the Fibonacci sequence. Can you identify the rule and determine the missing number? 

Riddle 2: The Age Puzzle

Tom is twice as old as Anna was when Tom was as old as Anna is now. If the sum of their ages is 36, how old are Tom and Anna?
Hint: Set up equations based on the relationships described in the riddle to solve for Tom's and Anna's ages. 

Riddle 3: The Lock Combination

I have a 3-digit lock that requires a specific combination to open. The digits are between 0 and 9, and each digit is unique. If I tell you that the sum of the digits is 14 and the product of the digits is 72, can you figure out the combination?
Hint: Use trial and error along with logical reasoning to determine the three unique digits that satisfy the given conditions. 

Riddle 4: The Chessboard Challenge

A standard chessboard has 64 squares. If I place 2 pennies on the first square, 4 pennies on the second square, 8 pennies on the third square, and continue doubling the number of pennies for each subsequent square, how many pennies would be on the 64th square?
Hint: This riddle involves understanding exponential growth. Calculate the total number of pennies accumulated on each square to find the answer.

Riddle 5: The Water Jug Puzzle

You have two empty jugs: one that can hold 3 litres and another that can hold 5 litres. How can you measure exactly 4 litres of water using these two jugs?
Hint: This classic puzzle requires creative use of the two jugs and understanding of basic arithmetic operations (addition and subtraction). 

Triangle Properties:

Challenge: Given a triangle with sides of lengths 𝑎=5, b=12, and 𝑐=13 determine whether it is a right triangle.

Circle Theorems:

Challenge: Given a circle with centre O and radius r=6 units, find the circumference and area of the circle.

Volume Calculations:

Challenge: Calculate the volume of a cube with edge length s=4 units.

Polygon Angles:

Challenge: Determine the sum of the interior angles of a hexagon (6-sided polygon).

Mental Arithmetic:

Long Multiplication: 456 × 73 | 345 × 78

Square Root Extraction:  √784 | √4096 |√149769

Arithmetic Word Problem:
Problem: Alice has 3 times as many apples as Bob. If Bob has 5 apples, how many apples does Alice have? 

Percentage Word Problem:
Problem: A shirt originally priced at $40 is on sale for 20% off. What is the sale price of the shirt?

Rate and Distance Word Problem:
Problem: Sam drives at an average speed of 60 miles per hour. How long will it take him to drive 180 miles? 

Algebraic Word Problem:
Problem: The sum of two consecutive integers is 25. Find the integers. 

Geometry Word Problem:
Problem: Find the area of a rectangle with length 10 units and width 6 units.

Probability Word Problem:
Problem: A bag contains 5 red marbles and 3 green marbles. If a marble is drawn at random from the bag, what is the probability of drawing a red marble? 

Finance Word Problem:
Problem: If Sarah invests $500 in a savings account with an annual interest rate of 4%, how much will she have after 3 years (assuming interest is compounded annually)?

Number Sequences

What type of sequences are there below? Can you work out any numbers that come after any of the numbers in any of them?

   - Example: (2, 5, 8, 11, 14)

   - Example: (3, 9, 27, 81, 243)

   - Example: (0, 1, 1, 2, 3, 5, 8, 13, 21)

   - Example: (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)

   - Example: (1, 4, 9, 16, 25, 36, 49, 64, 81, 100)

   - Example: (1, 3, 6, 10, 15, 21, 28, 36, 45)

   - Example: (1, 1, 2, 6, 24, 120, 720)
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