Coding⏱️ 2 min read📅 2026-05-31

How to Fix: Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing

Find the missing number(s) in a sequence of numbers from 1 to 100, given exactly k are missing.

Quick Answer: Use the formula for the sum of an arithmetic series: n(n+1)/2. Calculate this sum and subtract it from the total sum of numbers from 1 to 100 (which is also n(n+1)/2) to find the missing number(s).

The problem of finding the missing number(s) in a sequence from 1 to 100, given that exactly k numbers are missing, is more complex than initially perceived. The initial naive approach of calculating the sum of the first N natural numbers does not directly apply when there are missing values.

⚠️ Common Causes

  • Assuming the sequence is continuous and every number from 1 to 100 appears exactly once.

🛠️ Step-by-Step Verified Fixes

Method 1: Using the Sum of Arithmetic Series Formula

  1. Step 1: Calculate the total sum of numbers from 1 to 100 using the formula for the sum of an arithmetic series: S = N * (N + 1) / 2, where N is the last number in the sequence. For this problem, S = 100 * (100 + 1) / 2.

Method 2: Finding Missing Numbers Directly

  1. Step 1: Calculate the sum of numbers from 1 to k, where k is the number of missing values. This represents the total value that should be present in the sequence if all numbers were there.

💡 Conclusion

To find the missing number(s), subtract the sum of numbers from 1 to k from the total sum of numbers from 1 to 100. This will give you the value that is missing in the sequence.

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