Math Olympiad Tricks | Nice Exponent Math Simplification | Algebra Problem
2024 ж. 27 Нау.
4 250 Рет қаралды
Hello,
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In this Math Olympiad Algebra Problem, you'll learn tips and tricks of solving International Math Olympiad exams quickly. #IMO #matholympiad #algebra #radicalequations #simplify #exponential
Coming from CS, my first idea was to convert all the numbers to binary, add them, then convert back to decimal, you only double each value or add 1 at each step, more tedious but I believe it’s quicker
Thanks 👍😊 for your input and support
Agree 100%, you end up doing sums anyway, with or without the calculator.
To keep numbers factored avoiding large numbers: 2^15 + 2^12 + 2^9 + 2^6 + 2^3 = 2^3 · [ 2^12 + 2^9 + 2^6 + 2^3 + 1 ] = 2^3 · [ 2^12 + 2^9 + 2^6 + 2^3 + 1 ](2^3-1) / (2^3-1) = 2^3 · [ 2^12 (2^3-1) + 2^9 (2^3-1) + 2^6 (2^3-1) + 2^3 (2^3-1) + 1 (2^3-1) ] / (8-1) = 2^3 · [ 2^15 - 2^12 + 2^12 - 2^9 + 2^9 - 2^6 + 2^6 - 2^3 + 2^3 - 1 ] / 7 = 2^3 · [ 2^15 - 1 ] / 7 = 8 · 32767 / 7 = 8 · 4681 = 37448
Math Olympiad Tricks: 2¹⁵ + 2¹² + 2⁹ + 2⁶ + 2³ = ? 2³(2¹² + 2⁹ + 2⁶ + 2³) + 2³ = (2³)(2³)(2⁹ + 2⁶ + 2³ + 1) + 2³ = (2³)(2³)(2³)(2⁹ + 2⁶ + 1) + (2³)(2³) + 2³ = (2³)(2³)(2³)(2³)(2³ + 1) + (2³)(2³)(2³) + (2³)(2³) + 2³ = (2³)(2³)(2³)(2³)(2³ + 1) + (2³)(2³)(2³ + 1) + 2³ = (2³ + 1)(2³)(2³)[(2³)(2³) + 1] + 2³ = (9)(64)(65) + 8 = (9)(60 + 4)(60 + 5) + 8 = (9)[3600 + (9)(60) + 20] + 8 = 32400 + 4860 + 180 + 8 = 37488
Terimakasih telah membantu
You're welcome 😊
A simple brute-force method done in my head is the fastest: 8+64+512+4096+32768=37448