Math Problem Statement

Below is a number pyramid where the numbers are arranged in a logical fashion so you can replace each question mark with a correct whole number. Determine what that logic is and find each missing number.

Solution

The pyramid puzzle involves determining the missing numbers by identifying the logic that connects the numbers. In such puzzles, the number in each box is often derived from a specific relationship between the numbers directly below it. A common rule in number pyramids is that the number in each box is the sum or a mathematical combination (e.g., sum, difference) of the two numbers directly below it.

Let's break this down:

  1. We know the number at the top of the pyramid is 72.
  2. Looking at the row below it, we have two missing numbers that should add up to 72.
  3. The next row gives us 29, 12, and 31.
  4. The base row provides us with 20, 3, and 16.

From here, we can work upwards using the likely rule: each number is the sum of the two numbers directly beneath it.

Let's begin calculations step-by-step:

  • The number above 20 and 3 should be 20+3=2320 + 3 = 23.
  • The number above 3 and 16 should be 3+16=193 + 16 = 19.
  • The number above 23 and 19 should be 23+19=4223 + 19 = 42.

Now for the next step:

  • The number above 29 and 12 should be 29+12=4129 + 12 = 41.
  • The number above 12 and 31 should be 12+31=4312 + 31 = 43.

Finally:

  • The number at the top should be the sum of the two numbers directly below it, which would be 41+43=8441 + 43 = 84, but we are given that this number is 72, suggesting there is a different relationship at the higher levels. We can recheck the logic for top rows.

Would you like me to continue refining this approach?

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Math Problem Analysis

Mathematical Concepts

Addition
Patterns
Number Pyramids

Formulas

Sum of adjacent numbers to form the number above

Theorems

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Suitable Grade Level

Grades 6-8