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Questions tagged [mental-arithmetic]

Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.

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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 ...
Sny's user avatar
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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\...
Kai's user avatar
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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 ...
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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., ...
user366312's user avatar
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1 vote
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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.
yumham's user avatar
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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 ...
Satvik Duddukuru's user avatar
1 vote
0 answers
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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/...
Emperor Concerto's user avatar
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 ...
Oriom Lyra Lisboa's user avatar
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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 : ...
Aritro Shome's user avatar
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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 ...
24n8's user avatar
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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, ...
Todd Messenger's user avatar
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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 $...
Albus Dumbledore's user avatar
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1 answer
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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 ...
tchappy ha's user avatar
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2 votes
3 answers
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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. ...
Matthew S.'s user avatar
3 votes
4 answers
309 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 ...
M.Ross's user avatar
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Mental arithmetic: Add numbers by combining numbers that add up to 10

I'm reading a book on mental arithmetic, and came across this paragraph: You were taught - or should have been taught - at school that speed in addition is acquired by combining pairs of successive ...
datguyray's user avatar
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I want to learn math do I need to memorise the times tables?

As a front end developer, I do not need Math, however, I want to seriously learn it so that, maybe, one day, I might be able to get so good at it as to get into AI. I started with Algebra 1 and ...
relidon's user avatar
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1 answer
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Whats best method to calculate multiplication mentally?

I would like to know which method is better for mentally multiplication calculation between a) Cross-Multiplication and b) Left-to-Right Multiplication Thank you!
valentin 1990's user avatar
6 votes
1 answer
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How many digits are there in $99^{99}$? [duplicate]

Question: How many digits are there in $99^{99}$? My attempt: Observe that $$99^{99} = (100\times 0.99)^{99} = 100^{99}\times 0.99^{99}.$$ Note that $100^{99} = 10^{198}$ has $199$ digits and $$0....
Idonknow's user avatar
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Calculate $2^{5104} \bmod 10$ using mental arithmetic

I am practising interview for Jane Street's trader internship and I found the following question. Question: Calculate $2^{5104} \bmod 10$ using mental arithmetic. I know that $2^5 \bmod 10 \...
Idonknow's user avatar
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1 vote
1 answer
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Determine the number of digits of the product a.b

If $ a = 3,643,712,546,890,623,517 $ and $ b = 179,563,128 $, determine the number of digits of the product $ a.b $. I went searching the site and found this post where advise to use logarithm ...
Helen's user avatar
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Are there techniques for quickly seeing patterns in numbers?

Recently I was watching 8 out of 10 cats does countdown (S18E01 - 26 July 2019), for which the math question there was the following numbers: if you haven't seen countdown, you are provided 6 numbers,...
alexjiaoliu's user avatar
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1 answer
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are combinatorics-leaning mathematicians very good at mental math? [closed]

a common cliché in movies is that mathematicians who specialize in combinatorics are very adept at mental math (arithmetic), is that a real thing? if yes why?
Simo's user avatar
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1 answer
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Can a mental calculator plot any function in seconds? [closed]

As we learnt at school, to draw the graph of a function in details it may be necessary to perform some steps of calculation such as finding domain and codomain, limits, asymptotes and sign of ...
sound wave's user avatar
2 votes
2 answers
1k views

How do you calculate bitwise XOR in your head?

Subtraction has an easy method: you can literally count down until you get it. So does addition, multiplication, division, etc. However, does bitwise XOR have a method like this that you can do in ...
virchau13's user avatar
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1 vote
1 answer
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Mental techniques for large arithmetic and decimals

Consider the following problems: $$\frac{14}{4.6\dot{6}}$$ $$20 \cdot 45$$ $$\frac{7}{6}$$ $$28 \cdot 0.28$$ $$\frac{42}{168}$$ I'm looking for some techniques to solve these problems fast without ...
mr-matt's user avatar
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1 answer
159 views

Efficient modular reduction of integers in radix representation

I'm trying to find an easy and fast way to get the result of $$353094232\bmod721$$ I would solve this by dividing manually the terms until I get the remainder of dividing, but I was wondering if there ...
Dave Venturini's user avatar
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Estimating square numbers

A large dice has a side length of 9.2 cm. Estimate the surface area of the cube. What I did: 6× $9^2$ = 6 × 81 = 6 × 80 = 480 But the answer says that $9.2^2$ is 85 as an estimate. How do I get ...
user12345's user avatar
1 vote
2 answers
108 views

What would be the best way to memorize the 10 by 10 multiplication table?

Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
user avatar
1 vote
0 answers
114 views

Mental approximations of 1) log, 2) non-integer power

I am currently preparing for a interview that is notorious for asking mental approximations. Two example questions came up: 1) $\ln 514$ and 2) $3^{3.6}$. What are some of the best ways to calculate ...
user107224's user avatar
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4 votes
4 answers
1k views

What method for mentally computing 2-digit multiplication problems, minimizes the amount of mental steps?

So I've been practicing alot of mental math recently and ofcourse as a part of that, multiplying a double-digit number by another double-digit number. I have been doing some research into what the ...
Charlie Shuffler's user avatar
-1 votes
1 answer
1k views

Vinculum number of 989?

To find vinculum number I was subtracting finding the complement of 989 and cosidering the number to be 0989 I raised the 0 to 1 so my answer was 1011 , but why was the answer given 1111 ? Do I also ...
Chloritone_360's user avatar
-1 votes
2 answers
314 views

Age questions: How to approach solving this?

Completely foxed by this question: Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as Moses will be when Moses is as old as Methuselah is now. The difference in their ...
senna_ananth's user avatar
0 votes
2 answers
361 views

Generating "random" mental calculation exercises?

I recently tried to come up with "random" mental calculation exercises in an attempt to fight traffic jam boredom. Unfortunately, I quickly got bored by the lack of creativity of the problems I can ...
bluenote10's user avatar
0 votes
2 answers
334 views

How many zeros will $ 3^{3}4^{4}5^{5}6^{6} - 3^{6}4^{5}5^{4}6^{3}$ ends with?

I have this GRE practice question, asking me to find the quantity $$ 3^{3}4^{4}5^{5}6^{6} - 3^{6}4^{5}5^{4}6^{3}$$ will end in how many zeros? The answer given is $4$, but I don't quite understand ...
OGC's user avatar
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29 votes
3 answers
3k views

How to find a volume of this figure (which is $3080 \text{ cm}^3$) in a few seconds?

I was watching this Japanese game show and came across this question: The contestants were told that each small cube is 2cm on its side and were asked to find the volume of the above figure. The ...
Maru's user avatar
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2 answers
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Multiplication tables: up to what number should I memorise? [closed]

I never memorised them and suffered immensely through school as a result. Eg. I calculated 7x8 as (7x10=70) minus 7 using my fingers (63) then minus again on my fingers (56). In Australia children ...
Humanities Guy's user avatar
2 votes
3 answers
408 views

Why is it so good to know that $(1+x)^n \approx 1+nx$ for $nx \ll 1$?

I’ve often heard that it’s good to memorize the fact that $(1+x)^n \approx 1+nx$ for $nx \ll 1$ (most recently here), especially for mental arithmetic or making quick approximations. But why? Could ...
Ben Kovitz's user avatar
1 vote
3 answers
217 views

What is the method for mentally computing $3^{3.5}$ and similar calculations?

What is the method for mentally computing an approximation of $3^{3.5}$ and similar calculations? (without using any calculator) The best I did is: $3^{3.6}=e^{3.6ln(3)}=e^{3.6*1.098} \approx e^{3.6*...
astudentofmaths's user avatar
0 votes
4 answers
630 views

Without using a calculator how to solve $x^x = 100$? [duplicate]

Without using a calculator how to solve $x^x = 100$ ? A way of finding an approximation to 2 decimals would be good neough. I know about the Lmabert W function but one cannot compute it mentally. ...
astudentofmaths's user avatar
2 votes
1 answer
425 views

How can I best mentally calculate the total sum of a sequence of linear increases?

I often run into the following situation: In January, I'm producing $10$ items/month. By December, I want to be producing $65$ items/month. So assuming things improve linearly, my production is ...
NudeCanalTroll's user avatar
3 votes
2 answers
3k views

I want to learn math from basics the Indian way and am looking for a book to guide me and some workbooks to practice. Any recommendations?

I was taught math in a very stoic method during my childhood and as a result became math-phobia. Now as an adult, I wish to relearn math as a long term hobby and a cure for my phobia. I found that in ...
user avatar
7 votes
1 answer
557 views

Mentally generating a (pseudo)random {0,1}-sequence with uniform distribution

I want to learn of good ways by which to generate $\{0,1 \}$-sequences in my head which are (pseudo)random with uniform distribution, so that I may simulate flipping a fair two-sided, standard coin. I ...
user173897's user avatar
1 vote
1 answer
671 views

Proof behind this mental math multiplication?

Recently came across this technique of multiplying two $2$-digit numbers involving the same digit at the tens place and the sum of digits at units place being $10$. E.g., $73 X 77$ has same digit at ...
user avatar
4 votes
6 answers
584 views

Why doesn't $26\times 24 = 25\times 25?$ (I remove and $+1$ from both numbers) [closed]

I'm solving a math puzzle: "how quickly can you multiply $26$ by $24?$" I don't know the answer so I use tutorials. One tutorial say to do it quickly you can round numbers up and down to closest ...
bodacydo's user avatar
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7 votes
3 answers
6k views

(Quickly) finding the smallest fraction

Please see these fractions: (A) $\frac{33}{128}$ (B) $\frac{45}{138}$ (C) $\frac{53}{216}$ (D) $\frac{83}{324}$ (E) $\frac{15}{59}$. I need to find out quickly (in about a minute) the smallest of ...
Masroor's user avatar
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2 votes
2 answers
79 views

Mental division of two fractions?

I've got a non-calc paper coming up, and when going through a test, this fraction came up: $$ \frac{8}{-0.4} \equiv \frac{8}{\big(\frac{-2}{5}\big)} $$ Going through the answers he says: $$8/2=4$$ ...
user avatar
1 vote
2 answers
54 views

Approximate this fraction (simple arithmetic)

If I have $1.5\cdot10^{-5}=\frac{1.5}{10^5}$ , how can I rewrite (approximate) this fraction as $$ \approx \frac{1}{66.7\cdot 10^3}\quad ? $$ My calculator gives the exact answer $\frac{3}{200000}$, ...
Donsert's user avatar
  • 451
5 votes
3 answers
208 views

Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?

We can raise a sum to the power of $n$ quickly and easily using Pascal's triangle, due to the binomial theorem: $$(a+b)^n = \sum_{i=0}^n {n \choose i} a^i b^i$$ For sums of more than one term, we ...
goblin GONE's user avatar
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0 votes
1 answer
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Mixture and Alligation:::

A solution contains alcohol and water in the ratio 3:1, 16 litres of the Mixture is drawn off and 12 litres of water is added.11 litres of Mixture is replaced by 11 litres of water.The alcohol and ...
cloud computing in salesforce's user avatar