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Solve the Pattern: 2, 4 -> 20, 3, 9 -> 90, 1, 7 -> ?
Published on September 8, 2024
Pre-Algebra
This math puzzle presents a pattern where two numbers are combined to produce a third. The pattern is to square each number, then add the results. For example, 2 and 4 become 20 because 2^2 + 4^2 = 20. The puzzle asks for the result of combining 1 and 7, which is 50.
Question
Answer
Let’s break down the pattern in this puzzle.
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Observation: It seems like the numbers at the top are being combined in some way to produce the number below.
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First Example (2, 4 -> 20):
- If we multiply the two numbers: 2 * 4 = 8. This isn’t 20.
- If we add the two numbers and then multiply by 2: (2 + 4) * 2 = 12. This isn’t 20 either.
- If we square the sum of the two numbers: (2 + 4)^2 = 6^2 = 36. Still not 20.
- If we add the squares of the two numbers: 2^2 + 4^2 = 4 + 16 = 20. This works!
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Second Example (3, 9 -> 90):
- Let’s test our theory from the first example: 3^2 + 9^2 = 9 + 81 = 90. It works again!
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Applying the Pattern (1, 7 -> ?):
- Following the pattern, we should square the numbers and add them: 1^2 + 7^2 = 1 + 49 = 50.
Answer: The missing number is **50 © **.