5
votes
3answers
124 views

What is the most mathematically sound way to define the “damage per second” for a weapon?

Consider a weapon firing shots every $f^{-1}$ seconds (i.e. $f$ is the weapon's fire rate). Each shot deals $n$ damage to is target. Consider another weapon firing every $3f^{-1}$ second, but dealing ...
23
votes
0answers
811 views

$4494410$ and friends

$4494410$ has the property that when converted to base $16$ it is $44944A_{16}$, then if the $A$ is expanded to $10$ in the string we get back the original number. ...
11
votes
1answer
103 views

Request for a proof of the following continued-fraction identity

I have been poring over many texts about continued fractions, but none of them seem to be helping me to prove the following beautiful continued-fraction identity (I am nowhere close): $$ ...
1
vote
1answer
235 views

Multiplication Table with a frame and picture of equal sum

Is there an $n \times n$ multiplication table such that if you form a border of width $k$ ("the frame") and sum its elements, the total will equal the sum of the remaining elements ("the picture")? ...
0
votes
0answers
131 views

Puzzle: Representing age using digits from birth-year in order. Impossible cases?

I recently wrote my friend a birthday card and thought it would be fun to write her age using mathematical operations on the digits of her birth-year in order. For example she turned 36 and was born ...
0
votes
1answer
155 views

how does the interesting number method work and always come up with 1089 [duplicate]

Possible Duplicate: a question about permutation in the digits in the decimal system I dont get how it works but the method is: think of a three didgit number with none of the same didgits ...
3
votes
2answers
100 views

Different Representations of Numbers in Subsets of $\mathbb R$

I think I've mentioned sometime before about logarithmic number system. In this system, a real number $r$ is represented by $(\text{sgn}(r), \log|r|) \in \{-1, 0, 1\} \times \mathbb R$. If $\mathbb R$ ...
1
vote
3answers
242 views

Need help with problem related to latitude and longitude coordinates

My husband's boss is taking all the sales team to a team building event in Denver, Colorado and he has been sending hints for the last week. Now he has sent a math problem and told us it has something ...
19
votes
5answers
719 views

a big number that is obviously prime?

I once heard it asserted that $91$ is the smallest composite number that is not obviously composite. The reasoning was that any composite number divisible by $2$, $3$, or $5$ is obviously composite, ...
3
votes
0answers
94 views

Least characters in a numerical representation of integers

I was wondering what the shortest way to represent any given number is. For example, $387420489=9^9$. So, for this case, the smallest representation is of order 2 (2 numbers). Alternatively, ...