Question

thinkwell homeschool
brain teaser #2
number patterns
can you find the value of the missing number in the diagram below?
1
1 1
1 2 1
1 3 3 1
1 4 4 1
1 5 10 10 5 1
?

Explanation:

Step1: Identify the pattern (Pascal's Triangle)

In Pascal's Triangle, each number (except the ones on the edges) is the sum of the two numbers directly above it. For example, in the third row (1, 2, 1), 2 = 1 + 1. In the fourth row (1, 3, 3, 1), 3 = 1 + 2 and 3 = 2 + 1.

Step2: Apply the pattern to the missing number

Looking at the row with the missing number: 1, 4,?, 4, 1. The number above the missing number (let's call it \( x \)) are 3 and 3 (from the row above: 1, 3, 3, 1). So, \( x = 3 + 3 \).

Answer:

6