Questions tagged [mental-arithmetic]
Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.
115
questions
0
votes
1
answer
34
views
Expected Length of Walk on Truncated Icosahedron
Consider a truncated icosahedron with 12 pentagons and 20 hexagons. Starting from a hexagonal face, we go to any neighboring polygon randomly with equal probability. What is the expected number of ...
- 151
0
votes
0
answers
97
views
How to quickly mentally calculate large powers for a single digit?
How do you calculate something like $9^{21}$ in your head quickly? Was asked this during an interview and did not know what is a good way to quickly derive the answer. The actual answer is $1.0941899\...
- 43
0
votes
1
answer
188
views
Does practicing mental math increase mathematical intuition? [closed]
Has any experienced mathematician on this site found that practicing mental math was associated with the development of mathematical intuition and conceptual understanding? I was considering ...
- 3,019
1
vote
1
answer
164
views
Can you propose any hack for remembering multiplication tables from $13-19$?
I memorized multiplication tables from $2-12$ when I was in elementary school.
Regarding tables $13-19$:
I remember some intermittent elements
I find others by multiplication by recombination. E.g., ...
- 1,671
1
vote
2
answers
529
views
Trick for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$
Are there any tricks for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$?
I guess it involves binomial expansion but it still seems too complicated.
- 13
0
votes
1
answer
42
views
Mental math to quickly solve a product of mixed numbers with variables
I've come across the following question: "Let $6\frac{1}{m}\times n\frac{2}{11}=21$, where m, n are natural numbers. Find m+n."
Outside of actually solving the question, I've tried to guess ...
1
vote
0
answers
73
views
How to quickly eyeball maximum sum subarray?
Given an integer array, I want to find the continuous subarray (containing at least one number) which has the largest sum. There are some algorithmic solutions to this here: https://en.wikipedia.org/...
- 1,415
1
vote
1
answer
215
views
An app for learning the 1-100 times tables
Do anyone knows an app for android that help you learn $1$ to $100$ times table? I tried a few but none was quite what I need. I want it to:
Ask answers for two digit by one digit multiplication. $23 ...
0
votes
0
answers
5k
views
In time t, a dog does 3 jumps whereas a fox does 5. If distance covered in a jump by a dog is thrice that of the fox, find ratio of speed of dog : fox
This looks (and I think it is) a pretty simple problem.
My reasoning is as follows :
...
- 361
0
votes
2
answers
2k
views
Sum of values from 1 to 100 excluding values with digits of 7 and/or 8
I want to quickly sum values from 1 to 100, but exclude values with digits of 7 and/or 8 (e.g., 7,8,17,18,70,78,....) from the sum.
This is a mental math problem that I want to do in a really quick ...
- 1,485
1
vote
4
answers
385
views
Is there a reasonably accurate and easy way to approximate lbs-stones or kg-stones (and vice versa)?
For example, when I need to talk with my American friends about body weight:
$\mathrm{KG}\times2+10\%$
($100\times2=200$, $200+10\%=220$... Pretty accurate and easy to do mentally, both ways)
However, ...
- 113
1
vote
1
answer
133
views
prove that $5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$ [duplicate]
prove that $$5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$$
.A little use of calculator shows that $\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}=5.44$.Thus the inequality is indeed true.
Generalising this result with $...
- 11.9k
1
vote
1
answer
198
views
Prove that $e^\pi > 21$. Without a proof, you can use the two facts: $e > 2.71$ and $\pi > 3.14$.
I heard that the following problem is for high school students.
Prove that $e^\pi > 21$.
Without a proof, you can use the two facts: $e > 2.71$ and $\pi > 3.14$.
My solution is the ...
- 8,750
2
votes
3
answers
549
views
How to solve a fraction with a numerator in exponential form and a denominator in numerical form without a calculator?
The question:
"Imagine unwinding (straightening out) all of the DNA from a single typical cell and laying it "end-to-end"; then the sum total length will be approximately $2$ meters. ...
- 268
3
votes
4
answers
310
views
Multiplication of decimal numbers
I was wondering if anyone knows any good resources to use or tricks to be able to solve these kinds of mental-arithmetic questions(See image below)? Would be really grateful for any help !
Edit: I ...
- 31