How to Fix: Quickest way to find missing number in an array of numbers
Find missing number in an array of numbers from 1 to 100 with a random empty slot.
📋 Table of Contents
The problem of finding a missing number in an array is a classic example of a mathematical puzzle. Given an array of numbers from 1 to 100, where one random empty slot exists, the quickest way to find that slot and the number that should be put in it involves utilizing the properties of the sum of an arithmetic series.
🔍 Why This Happens
- The total sum of numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series: n*(n+1)/2, where n is the last number in the sequence.
- Since one random empty slot exists, the actual sum of the array will be less than the expected total sum by the value that should fill the missing slot.
🛠️ Step-by-Step Verified Fixes
Method 1: Sum of Arithmetic Series
- Step 1: Calculate the total sum of numbers from 1 to 100 using the formula n*(n+1)/2, where n = 100.
Method 2: Find the Missing Number
- Step 1: Calculate the actual sum of the array by iterating through each number and adding it to a running total.
- Step 2: Subtract the expected total sum from the actual sum to find the value that should fill the missing slot.
💡 Conclusion
By utilizing the properties of the sum of an arithmetic series, you can quickly find the missing number in the array and determine what value should fill the empty slot.
❓ Frequently Asked Questions
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