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Results tagged with number-theory
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user 11110
A mathematical puzzle whose solution is heavily based on the arithmetic properties of the integers. Use with [mathematics]
5
votes
Accepted
6
votes
Accepted
Find the value of $\bigstar$: Puzzle 2 - Switch-a-roo
Explanation:
Addendum:
Mike Earnest mentions another possibility; because the symbols must be integers, but the 'intermediate' results not,
The addendum applies here as well.
- 28.2k
5
votes
Accepted
Find the value of $\bigstar$: Puzzle 4 - In Between
Solution:
Explanation:
Proof of assumption A:
- 28.2k
4
votes
Accepted
4
votes
15
votes
Accepted
An Accountant Seeks the Help of a Mathematician
The mathematician owes
and the other faculty members owe
Explanation:
Table:
- 28.2k
11
votes
Accepted
3
votes
Find the value of $\bigstar$: Puzzle 3 - Substitution
Explanation ('brute-force' substitution, there's probably a more elegant solution):
- 28.2k
5
votes
Accepted
10
votes
3
votes
Sum of digits of sum of digits of sum of digits
Well, given that
and we only need to find
The format of question seems to imply the other answers must be wrong.
- 28.2k
16
votes
Accepted
My Social Security Card Number
I think the answer is
Proof:
It's a bit like:
See the following table:
So we can make
In theory, we want
Concatenating all the pairs we get the answer:
- 28.2k
42
votes
Accepted
First digit of 3^2020
I think it's a
Explanation:
According to my calculator (this answer was posted before the no-computers tag was added),
If we're not allowed to use computers, I would
The same trick is used …
- 28.2k