Rocket Ship Number Patterns Quiz

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Questions and Answers

What mathematical operation was used on the first fin of the first rocket to find the body number?

Division followed by squaring (correct)
Subtraction
Addition
Multiplication

What prime factor combination balances the first rocket ship's numbers?

2 x 3 = 6 with 4 x 9 = 36 (correct)
2 x 2 = 4 with 6 x 9 = 54
3 x 3 = 9 with 2 x 4 = 8
2 x 3 = 6 and 3 x 4 = 12

How do you find the body number of the third rocket ship?

By squaring the first fin and dividing by the second fin (correct)
By dividing the result of the first fin squared by the nose
By adding the fins and the nose
By multiplying the first fin and the nose

What was the resulting body number found for the third rocket ship?

<p>6 (C)</p> Signup and view all the answers

Which method was validated by the calculations for the second rocket ship?

<p>Taking the first fin to the power of the nose equals the product of the other two numbers (C)</p> Signup and view all the answers

Flashcards

What is the goal of the rocket ship puzzle?

The goal of the rocket ship puzzle is to find the missing body number in the third rocket ship using the pattern found in the first two. The pattern involves finding a connection between the numbers in each ship. For example, the prime factors of the fins and nose must be balanced by the product of the body and other side fin.

What is the pattern in the rocket ship puzzle?

The pattern in the rocket ship puzzle requires finding a relationship between the numbers in each ship. The numbers in each ship represent the prime factors of the different parts of the rocket. The product of the fins and nose's factors must equal the product of the body and other fin's factors, implying a need to balance the prime factors.

How to find the missing number in the 3rd rocket ship?

The missing number in the third rocket ship can be found by applying the pattern found in the first two ships. The pattern involves taking the left fin to the power of the nose. This result should equal the product of the other fin and the body.

Explain the prime factorization concept in the rocket ship puzzle?

The pattern in the rocket ship puzzle is based on the concept of prime factorization. Each number is effectively broken down into its prime factors, and the pattern involves balancing these factors across the different parts of the rocket ship. For example, after finding the prime factorization of each number, multiply the prime factors of the fins (left and right) and nose to ensure it equals the prime factors of the body and other fin.

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What is the missing number in the third rocket ship?

The missing number in the third rocket ship is 6. This is found by applying the pattern established in the first two rocket ships. The pattern involves taking the left fin to the power of the nose and equating it to the product of the other fin and the body. In the third rocket ship, 12^2 = 144, and dividing 144 by the second fin, 24 gives 6.

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Study Notes

The Puzzle

A puzzle with three rocket ships, each containing four numbers
The two fins, the nose, and the body of each rocket ship represent numbers
The goal is to find the missing body number in the third rocket ship using the pattern found in the first two

Pattern Explanation

The pattern involves finding a connection between the numbers in each ship
In the first ship, 6/2 = 3, and 3² = 9
This suggests dividing the left fin by the nose and squaring the result to get the body
This pattern doesn't apply to the second ship
The prime factorization of numbers in the first ship: 6 = 2 x 3, 9 = 3 x 3, 4 = 2 x 2, and 2 = 2
Combining prime factors of left fin and nose with body and right fin yields equal prime factors on both sides
To balance prime factors, squaring 6 results in 36, equal to 9 x 4

Applying the Pattern

Applying the pattern to the second rocket ship
Taking the left fin (4) to the power of the nose (3) gives 4³ = 64
Multiplying the body (2) and the right fin (32) also results in 2 x 32 = 64
Thus, the pattern holds: left fin raised to the power of the nose equals the product of the body and the other fin