Puzzles

Notes

• Used extended Euclidean algorithm
• Uses and demonstrates factor substitution method well

A good example of usage of modulus arithmetic.  

Hippocrates of Chios solved this, nearly 100 years before Euclid even wrote The Elements, and before we knew the exact formula for the area of a circle. This is said to be the first precise mathematical of the area between two curved lines. Learn how he solved for the area of a crescent-shaped lune (same Latin root as luna for moon). And I hope this will inspire you to solve a problem today that students thousands of years from now will learn in grade school.

• 536 Puzzles and Curious Problems

Research Links

• 536 Puzzles and Curious Problems

A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

Excel Spreadsheet method

• The first sheet uses a brute force method of stepping through all the values from 00.00 to 99.99 and looking for an integer solution
• The second sheet uses the relation below to drive towards a less brute force method
• The third sheet of the spread sheet shows how the solution is periodic like a set of gears.  The constant term added is represented as the column offset number and is analogous to a number of teeth offset from zero position at the start of turning of the gears.
• The fourth sheet uses 5 and 7 to simplify the problem