Problem Solving
... 35. A castle in the far away land of Notsuoh was surrounded by four moats. One day the castle was attacked and captured by a fierce tribe from the north. Guards were stationed at each bride over the moats. Johann, from the castle, was allowed to take a number of bags of gold as he went into exile. H ...
... 35. A castle in the far away land of Notsuoh was surrounded by four moats. One day the castle was attacked and captured by a fierce tribe from the north. Guards were stationed at each bride over the moats. Johann, from the castle, was allowed to take a number of bags of gold as he went into exile. H ...
4.5 Multiplying and Dividing Mixed Numbers Caution: is not the
... From this process, we come up with a quicker way to convert a mixed number to an improper fraction. Shortcut for Converting a Mixed Number to an Improper Fraction 1) If the mixed number is negative, hold the negative sign off to the side. 2) Multiply the integer part by the denominator of the fracti ...
... From this process, we come up with a quicker way to convert a mixed number to an improper fraction. Shortcut for Converting a Mixed Number to an Improper Fraction 1) If the mixed number is negative, hold the negative sign off to the side. 2) Multiply the integer part by the denominator of the fracti ...
7-1 Integer Exponents
... Notice the phrase “nonzero number” in the previous table. This is because 00 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above in the table with a base of 0 instead of 5, you ...
... Notice the phrase “nonzero number” in the previous table. This is because 00 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above in the table with a base of 0 instead of 5, you ...
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.