User RobPratt - Mathematics Stack Exchange

56 votes

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What is the optimal number of dice to roll a Yahtzee in one roll?

answered Feb 6, 2020 at 19:28

42 votes

What is the closed form of the $f$ with $f(1)=1$, $f(2)=7$ and $f(n)=7f(n-1)-12f(n-2)$ ($n\ge 3$)?

answered Jul 14, 2019 at 3:55

24 votes

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Is there a generating function for any finite sequence of random numbers?

answered Apr 7, 2020 at 22:05

23 votes

Can we arrange $\{1,...,16\}$ in $4\times 4$-grid so {products of rows} = {products of columns}?

answered Jan 22, 2020 at 18:46

15 votes

Number of ways to label die with opposing faces summing to 7

answered Jan 1, 2020 at 20:25

14 votes

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Does it exist a way how to find the ways to get from one point to another when certain points must be avoided in a grid?

answered Mar 21, 2020 at 1:56

14 votes

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How to geometrically determine number of holes for a triangle

answered Dec 17, 2022 at 4:40

12 votes

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Faster approach: Find the smallest integer $a$ such that $P = a\cdot1!\cdot2!\cdot3!\cdot4!\cdot5!....\cdot18!$ is a perfect square.

answered Jun 2 at 20:41

12 votes

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Express $\sum_{j=1}^{n}\sum_{i=1}^{n} \frac{1}{i(i+j)}$ in terms of harmonic numbers

answered Jul 16, 2019 at 3:22

11 votes

With $x_1^2+3x_2^2+2x_1x_2=32$, find max value of $|x_1-x_2|$

answered Jul 4, 2022 at 3:41

10 votes

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Can $\sin^2(x) = \cos^2(x) -1$

answered Mar 2 at 20:16

9 votes

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How to calculate this sum $\sum_{n=1}^{\infty} \frac{H_n \cdot H_{n+1}}{(n+1)(n+2)}$

answered Feb 11 at 19:27

9 votes

Choose signs such that $\pm\sqrt{1}\pm\sqrt{2}\pm\dots\pm\sqrt{2022}$ is as close as possible to $0$.

answered Jan 17, 2022 at 20:29

9 votes

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What is the longest path in a $3×3×3$ cubic lattice?

answered Feb 21, 2023 at 2:58

9 votes

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is it possible to divide $9\times 11$ rectangle into one $1\times 3$ rectangle and N tetrominoes?

answered Jan 16, 2020 at 22:25

8 votes

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Is a closed form for quaternary sequences avoiding some patterns known?

answered Jan 13, 2020 at 5:31

8 votes

Series prove using combinational argument

answered Jan 25, 2020 at 7:25

8 votes

Different bricks making a cube

answered Mar 23, 2020 at 1:56

8 votes

Show $\sum_{k=1}^{2n-1}\frac{\left(-1\right)^{k-1}k}{\binom{2n}{k}}=\frac{n}{n+1}$

answered Mar 12, 2020 at 17:58

8 votes

How many meetings would it take for 12 people to meet in 4 groups of 3 until they met everyone?

answered Dec 31, 2020 at 21:31

8 votes

Minimum number of straight lines to cover $n \times n$ grid?

answered Aug 31, 2023 at 1:21

8 votes

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Why does packing exactly 992 circles in a square behave exceptionally?

answered Nov 27, 2022 at 3:44

8 votes

What's the size of the biggest set of numbers from 1 to 100 so that no number is the average of any other two?

answered May 25, 2022 at 23:13

7 votes

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Re-arrangements of $(1,1,2,2,3,3,4,4)$ with $(1,2,3,4)$ as a subsequence

answered Aug 17, 2023 at 1:54

7 votes

Tuple notation for non-negative integers

answered Mar 30, 2023 at 3:15

7 votes

Accepted

What does min max in optimization problems mean?

answered Sep 11, 2020 at 1:12

7 votes

Triple Summation of product of Binomial Coefficients $\sum_{k=0}^n\sum_{j=0}^n\sum_{i=0}^n\binom ni\binom{n-i}j\binom{n-j}k=5^n$?

answered Apr 14, 2020 at 22:21

7 votes

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Summation with exclusion

answered Jan 17, 2020 at 4:10

6 votes

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Sum of a sequence.

answered Jul 15, 2019 at 20:49

6 votes

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counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$

answered Sep 22, 2019 at 22:28

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1,962 Answers

What is the optimal number of dice to roll a Yahtzee in one roll?

What is the closed form of the $f$ with $f(1)=1$, $f(2)=7$ and $f(n)=7f(n-1)-12f(n-2)$ ($n\ge 3$)?

Is there a generating function for any finite sequence of random numbers?

Can we arrange $\{1,...,16\}$ in $4\times 4$-grid so {products of rows} = {products of columns}?

Number of ways to label die with opposing faces summing to 7

Does it exist a way how to find the ways to get from one point to another when certain points must be avoided in a grid?

How to geometrically determine number of holes for a triangle

Faster approach: Find the smallest integer $a$ such that $P = a\cdot1!\cdot2!\cdot3!\cdot4!\cdot5!....\cdot18!$ is a perfect square.

Express $\sum_{j=1}^{n}\sum_{i=1}^{n} \frac{1}{i(i+j)}$ in terms of harmonic numbers

With $x_1^2+3x_2^2+2x_1x_2=32$, find max value of $|x_1-x_2|$

Can $\sin^2(x) = \cos^2(x) -1$

How to calculate this sum $\sum_{n=1}^{\infty} \frac{H_n \cdot H_{n+1}}{(n+1)(n+2)}$

Choose signs such that $\pm\sqrt{1}\pm\sqrt{2}\pm\dots\pm\sqrt{2022}$ is as close as possible to $0$.

What is the longest path in a $3×3×3$ cubic lattice?

is it possible to divide $9\times 11$ rectangle into one $1\times 3$ rectangle and N tetrominoes?

Is a closed form for quaternary sequences avoiding some patterns known?

Series prove using combinational argument

Different bricks making a cube

Show $\sum_{k=1}^{2n-1}\frac{\left(-1\right)^{k-1}k}{\binom{2n}{k}}=\frac{n}{n+1}$

How many meetings would it take for 12 people to meet in 4 groups of 3 until they met everyone?

Minimum number of straight lines to cover $n \times n$ grid?

Why does packing exactly 992 circles in a square behave exceptionally?

What's the size of the biggest set of numbers from 1 to 100 so that no number is the average of any other two?

Re-arrangements of $(1,1,2,2,3,3,4,4)$ with $(1,2,3,4)$ as a subsequence

Tuple notation for non-negative integers

What does min max in optimization problems mean?

Triple Summation of product of Binomial Coefficients $\sum_{k=0}^n\sum_{j=0}^n\sum_{i=0}^n\binom ni\binom{n-i}j\binom{n-j}k=5^n$?

Summation with exclusion

Sum of a sequence.

counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$