52
votes
Accepted
After the funeral
So first is to note that
I’d imagine that Julia got nothing because
As it turns out,
To Agnes, I bequeath 12,000 pounds.
To Eli, I bequeath 201,000 pounds.
To Eric, I bequeath 95,000 pounds.
To ...
- 32.3k
39
votes
How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed
Well, here is how I would (and did) solve it:
First step: Without the « five + » constraint
Second step: Getting rid of some « + »
A solution we found:
Extra note: finding all solutions
- 1,131
36
votes
Accepted
30
votes
Accepted
What is a Chess Number™?
A Chess Number™ is a number that
Here are the results for chess numbers:
And for not chess numbers:
- 10.3k
28
votes
Accepted
How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed
Another way to think about it is to start with plus signs in all eight positions. The sums are equal at $15$. When you remove a plus sign you add
- 7,671
26
votes
Accepted
Largest number with no repeating digit pairs
I believe this is the largest number that meets that criteria:
Reasoning:
- 1,102
24
votes
Accepted
24
votes
Accepted
21
votes
Ten-digit number that satisfy divisibilty rules for 2,3,4,5,6,7,8,9,10&11
This is a good problem to attack by computer:
So I thought, how far can we go?
Code used (Python 3 IDLE):
- 21.9k
21
votes
How can four be the half of five?
If you make a pentagon,
/ \
|_|
and you cut it in half from top to bottom you get:
/| |\
|_| |_|
that is, you get two ...
- 319
19
votes
Accepted
Which two students spoke wrongly?
Okay so the first step is to realize that:
Also,
Hence,
Also, we see that
Eliminating all of those, we get that the answer is
- 7,490
17
votes
Accepted
17
votes
17
votes
Accepted
17
votes
Accepted
What is a BEN Number™?
Ok, so a Ben number is a number that
Proof:
The hints helped so:
1-
2-
3-
4-
5-
6-
7- What helped me
The largest BEN number is then
- 776
16
votes
Accepted
The largest Saturday number
The more common name for a Saturday number is
There is a good argument for believing that they cannot grow to any length:
The longest Saturday number is:
To be honest, I wrote a computer program to ...
- 50.8k
15
votes
Accepted
When should this question be answered?
I'm a very impatient person so I've decided not to wait around to post an answer at the right time which I think will be
Reasoning
- 133k
15
votes
Largest number with no repeating digit pairs
What is the correct answer depends on the number system that is used.
In Hexadecimal, a common thing to display data from computers, the highest number is (with a space separating each block)
In ...
- 251
14
votes
Accepted
What is a Heptagon Number™?
A Heptagon number is
For each listed number:
The numbers in the other column do not have this property.
- 10.9k
14
votes
What comes next in this sequence, and why?
OH MY GOD I just got it. Like, as I was looking at my own question. Boy do I feel silly.
The next number is
PHEW that was bugging the bejeezus out of me! Hahaha
- 321
14
votes
Accepted
Which famous mathematical constant can be celebrated on these dates?
The constant is
Because the dates are
- 13.4k
14
votes
Accepted
13
votes
Accepted
Multilanguage generalization of "What number is that? Asks Grandpa"
In Mandarin Chinese:
十二
and
二十
Am I cheating?
In Braille:
In Arabic:
In Sino-Korean Cardinal Numerals written in Hangul:
In Morse Code:
In Roman Numerals:
For Binaries if...
Note for Latin:
...
- 5,963
13
votes
Accepted
13
votes
When should this question be answered?
Having 5 divisors means
A standard number-theoretical way to observe this is
So what we need to do now is
Here is the code in Factor:
The output is
- 11.6k
13
votes
Scrabble with prime numbers!
This is a huge question, and I think people can help each other here so I'm going to start with some initial strategy:
I have set up this board:
Which allows for this move:
For a score of 2372 (...
- 15k
13
votes
13
votes
Which positive integers have at least one positive integer multiple such that the base 10 representation of that multiple has only even digits?
I think that the positive integers with this property are
Proof
- 133k
12
votes
Which two students spoke wrongly?
Since the actual question is: Can you find the two numbers? Which two students spoke wrongly?, technically no one has answered it! The right answer is:
Solution:
- 2,009
12
votes
Sort 10 clock numbers
Since we are only asked to sort, not give actual counts, there is an easy proof that
- 10.2k
Only top scored, non community-wiki answers of a minimum length are eligible