Grade 12 Math Riddles Challenge

Grade 12 Math Riddles Challenge

Solve the following math riddles. Show your work or explain your reasoning for full credit. These riddles require critical thinking and application of advanced mathematical concepts.

1. I am a sequence where the first term is 3, and each subsequent term is generated by squaring the previous term and adding 1. What is the fourth term in this sequence?

2. A father is 3 times as old as his son. In 10 years, the father will be twice as old as his son. How old is the son now? The son is   years old now.

3. You have two fair six-sided dice. If you roll them both, what is the probability that the sum of the numbers rolled is a prime number?

4. I am a three-digit number. My second digit is four times as big as the third digit. My first digit is three less than my second digit. What number am I?

Match each riddle with the correct geometric shape.

5. If a mathematician says, 'All squares are rectangles,' and 'No rectangles are circles,' does it logically follow that 'No squares are circles'?

6. A farmer needs to cross a river with a fox, a chicken, and a bag of grain. The boat can only hold the farmer and one other item. If left alone, the fox will eat the chicken, and the chicken will eat the grain. How can the farmer get all three across the river safely? Detail each step.