Math Problem Statement

The sum of two adjacent blocks gives the sum of the block above. What number would replace the question mark?

The sum of two adjacent blocks gives the sum of the block above. What number would replace the question mark?

Solution

To find the missing number that would replace the question mark in this pyramid, we follow the given rule: the sum of two adjacent blocks gives the block above.

Let’s start from the bottom row and work our way up:

  1. Bottom row:

    • The numbers are 18, 40, 30, and 44.
  2. Second row:

    • The block above 18 and 40 is 40, which satisfies 18 + 40 = 58.
    • The block above 40 and 30 is 122, which satisfies 40 + 30 = 70 (not relevant here but helps confirm the rule).
    • The block above 30 and 44 is 122, which satisfies 30 + 44 = 74.
  3. Third row:

    • We already know one number: 122.

Now let's determine the missing block directly above the 122 and the unknown block.

  • The topmost block (450) is the sum of the two blocks below it. Since the block to the left of the question mark is already determined as 122, we can set up the following equation:

450=122+?450 = 122 + ?

Solving for the question mark:

?=450122=328? = 450 - 122 = 328

Thus, the number that should replace the question mark is 328.

Would you like any further explanation or details?

Here are five related questions to explore the concept further:

  1. What if the rule was multiplication instead of addition for the blocks?
  2. Can you derive the numbers of the top block using different mathematical operations?
  3. How would this change if we had more layers in the pyramid?
  4. What happens if one of the numbers in the base changes?
  5. How does the shape of the pyramid affect the structure of the numbers?

Tip: Always double-check the relationships in these puzzles by working backward to ensure consistency across all blocks.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Addition
Basic Algebra

Formulas

Sum of two adjacent blocks: block_above = block_left + block_right

Theorems

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Suitable Grade Level

Grades 4-6