19
votes
10answers
3k views

Get $5$ by doing any operations with four $7$s

How can one combine four sevens with elementary operations to get $5$? For example $$\dfrac{(7+7)\times7}{7}$$ (though that does not equal $5$). I am not able to do this. Can you solve it or prove ...
41
votes
11answers
17k views

Can a piece of A4 paper be folded so that it's thick enough to reach the moon?

While procrastinating around the web I stumbled on a page that contained the image below, from cracked.com. I can't help but believe that this is false… Even though the article header says: ...
6
votes
2answers
100 views

Mental Arithmetic

This is very possibly not the best place to ask this, however it's the best I could find but please suggest anywhere else that might be better suited. I'm building a sort of challenge revolving ...
1
vote
1answer
145 views

Primes created by “n + digital-root(n)” sequences

I've looked at the sequences created by repeatedly adding the digital root of a number to the number until it becomes prime. This is the pseudo-code for the program I've used:   n = 0 ...
2
votes
0answers
115 views

Inserting +/- into 123456789…

I'm looking at a generalization of the problem of inserting + and/or - into the blocks $123456789$ and $987654321$ to create a formula for $100$, like this: $$123 - 45 - 67 + 89 = 100$$ $$9 - 8 + 7 ...
7
votes
2answers
209 views

Come up with some fun “equation Limericks”

We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks". A Limerick is a poem with five lines. The first, second, and fifth lines should have nine syllables each and ...
0
votes
0answers
141 views

Gauss' Summation Trick; Applications and Generalizations

I'm going to write an article about the summation trick attributed to Guass and its applications and generalizations. I'm sure you know what is the trick I mean: $1+2+\cdots+100=101+101+\cdots+101$ ...
1
vote
1answer
51 views

Finding the time taken by a flight

I came across a question today which is as follows: A Flight takes off at 2 A.M from northeast direction and travels for 11 hours to reach the destination, which is in northwest direction. Given ...
1
vote
1answer
303 views

How many $n$-disk legal configurations are there for the Tower of Hanoi?

This question comes from this homework assignment from ECS20 at UC Davis. How many $n$-disk legal configurations are there for the Tower of Hanoi? A "legal configuration" means that no disk is ...
22
votes
1answer
757 views

A strange little number - $6174$.

Take a 4 digit number such that it isn't made out the same digit $(1111, 2222, .. . $ etc$)$ Define an operation on such a four digit number by taking the largest number that can be constructed out of ...
0
votes
1answer
48 views

Automatic searches for solutions to a recreational problem

I would like to examine the relationship of 5 numbers. 3,38,5,x set equal to .8 using abstract algebra. Yes I know (5/(38+3))*8 and (3/(38+5))*11 are close but I'm doing this all the time and I'd like ...
12
votes
5answers
826 views

Simplify : $( \sqrt 5 + \sqrt6 + \sqrt7)(− \sqrt5 + \sqrt6 + \sqrt7)(\sqrt5 − \sqrt6 + \sqrt7)(\sqrt5 + \sqrt6 − \sqrt7) $

The question is to simplify $( \sqrt 5 + \sqrt6 + \sqrt7)(− \sqrt5 + \sqrt6 + \sqrt7)(\sqrt5 − \sqrt6 + \sqrt7)(\sqrt5 + \sqrt6 − \sqrt7)$ without using a calculator . My friend has given me ...
-1
votes
3answers
751 views

Hands of a clock forming certain angles

How many times to the hands of a clock form a 60 degree angle between noon and midnight on the same day? Firstly im not sure weather they require the second hand to be included. And secondly (excuse ...
-2
votes
4answers
178 views

Simple Math Problem

A bat and ball cost \$1.10. The bat costs a dollar more then the ball. How much does the ball cost? If this is not the correct place to ask a question like this please tell me and I will remove it ...
5
votes
3answers
204 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 ...
76
votes
1answer
3k views

$4494410$ and friends

The number $4494410$ 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. ...
12
votes
1answer
184 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
382 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
195 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
224 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
125 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
326 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
897 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
101 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, ...