Olympiad Practice
Challenge yourself with advanced problems.
Strategies for Success
Olympiad problems often look impossible but hide a simple pattern or trick. Vedic Math tools like Digit Sums, Last Digit Analysis, and Algebraic Identities are your best friends.
Pattern Spotting
• 11² = 121
• 111² = 12321
• 1111² = 1234321
Use these patterns to solve huge roots instantly!
Modular Arithmetic
Finding remainders is easy with "Negative Remainders".
2¹⁰⁰ ÷ 3?
2 is -1 mod 3.
(-1)¹⁰⁰ = 1. Remainder is 1.
Solved Examples
Example 1: Find the last digit of 3²⁰²⁵
• Powers of 3: 3, 9, 27, 81, 243... (Ends in 3, 9, 7, 1).
• Cycle length is 4.
• 2025 ÷ 4 leaves remainder 1.
• So it ends in the 1st number of the cycle: 3.
Example 2: Simplify (999998 × 999998) - 1
• Let x = 999998.
• Expression is x² - 1 = (x-1)(x+1).
• (999997)(999999).
• Use Nikhilam (Base 1000000): (-3) and (-1).
• 999996 | 000003.
• Answer: 999996000003.
