Test your mathematical lateral thinking skill with these three little puzzles from the new book by me and Des MacHale:
1. In a 100 metre race, athletes A, B and C all run at a uniform pace. If A beats B by 10 metres and B beats C by 10 metres, by how much does A beat C?
2. Move any one digit to make this equation true:
62 – 63 = 1
3. Find any three positive integers a, b, c such that a3 + b4 = c5
The answers and many more wonderful mathematical lateral puzzles are found in the book.
#1)A beats C By [10- (90*90)/(100)] metres=19 metres
#1) 10 + 10 – (10 * 10) / 100 = 19 metres
#2) 62 – 63 = 1 —> 2^6 – 63 = 1 😉
#3) For a = 256, b = 64 and c = 32 —> a^3 + b^4 = 256^3 + 64^3 = 2^24 + 2^24 = 2 * 2^24 = 2^25 = (2^5)^5 = 32^5 = c^5
However, these a,b and c values are not the only ones.
For a=3^14 * 5^16, b=2 * 3^10 * 5^12, c=3^8 * 5^10 —> a^3 + b^4 = c^5 also holds by a cruious observation of Pythagorean Theorem 🙂