the King’s Factor Year 12 questions 2
... the King’s Factor Year 12 questions 2 1. For each of the following statements either prove that it is true or give a counter-example to show that it is false: (a) The product of any two even numbers is a multiple of 4. (b) The product of any two even numbers is a multiple of 8. (c) The product of an ...
... the King’s Factor Year 12 questions 2 1. For each of the following statements either prove that it is true or give a counter-example to show that it is false: (a) The product of any two even numbers is a multiple of 4. (b) The product of any two even numbers is a multiple of 8. (c) The product of an ...
Sample Test for MTH1120 and higher
... E. An infinite number 6. Sixteen students in a dance contest have numbers 1 to 16. When they are paired up, they discover that each couple’s numbers add to a perfect square. What is the largest difference between the two numbers for any couple? A. 5 ...
... E. An infinite number 6. Sixteen students in a dance contest have numbers 1 to 16. When they are paired up, they discover that each couple’s numbers add to a perfect square. What is the largest difference between the two numbers for any couple? A. 5 ...
Math 475 Big Problems, Batch 2 Big Problem 7: Tulie Number
... This was a little boring, so she tried the following. First she picked some positive number. Then: • (a) She subtracted the whole number part from it. If the result was zero, she stopped. • (b) If it wasn’t zero, she took the reciprocal. The result always had a whole number part so she went back to ...
... This was a little boring, so she tried the following. First she picked some positive number. Then: • (a) She subtracted the whole number part from it. If the result was zero, she stopped. • (b) If it wasn’t zero, she took the reciprocal. The result always had a whole number part so she went back to ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.