1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, ...

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243 views

What is the 6th term of the sequence? [closed]

Sequence: ABC; 1A1B1C; 111A111B111C; 311A311B311C; ... What is the 6th term of the sequence? ...
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2answers
64 views

Need help modifying this binomial expansion

The binomial theorem states that $$(A+B)^n=\sum_{k=1}^{n}{n \choose k}A^{n-k}B^k$$ I need help expressing the following summation as a modified binomial expression: $$\sum_{k=1}^{n}n!{n-1\choose ...
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158 views

Trying to figure out the pattern in this series

I'm trying to figure out the rule that's producing the series below. The first column is the factorials $1!,2!,3!,4!,5!,6!$ But I can't figure out what else is going on. So I know the next row will ...
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1answer
25 views

Pattern finding of last few digit of a^b

The question is:Find the last two digits of 9^2013.(No calculators allowed to solve this question.) Options: (A)01 (B)29 (C)41 (D)81 (E)89 From this point,I will show my working, 9^2=81(Last Digit ...
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1answer
463 views

Number pattern prediction algorithm [duplicate]

Since childhood we are all familiar with the task of predicting the next number in a sequence. From something simple like, $2,4,6,...$ and $4,9,25,...$ to something more complex like, ...
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226 views

Triangular Numbers that are odd, less than 2000

The diagram below shows the $1$st, $2$nd, $3$rd and $4$th triangular numbers. (1 spot) : $1$ (3 spots) : $3$ (6 spots) : $6$ (10 spots) : $10$ The formula $n(n + 1)/2$ can be ...
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2answers
74 views

Evaluate an unknown operator

I have a simple question but I can't seem to be able to solve it. Given that: 25 ╧ 17 = 267 35 ╧ 23 = 373 45 ╧ 15 = 465 what is ...
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2answers
40 views

What is the general stragety for conjecturing a formula based off a pattern?

Is it simply to guess and evolve a answer until it gets closer or is there an approach? Ex: Find the formula for: $a_k = \frac{a_{k-1}}{2} + 1$ where $a_0 = 1$. One would go: $a_1 = 3/2, a_2 = ...
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4answers
164 views

How to represent the $n$th number in the sequence $1,3,5,7,1,3,5,7,\dots$ as a closed form?

I'm given the repeating sequence $1,3,5,7,1,3,5,7,\dots.$ I must determine a formula for the $n$th term of the sequence. I have tried the triangle method, but since this is a repeating series it is ...
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3answers
111 views

Given the sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for it?

Given a sequence $3, 4, 11, 16, 42\ldots $ how can I derive a general formula for this sequence? Is there any optimised approach? My approach: the given series is equal to summation of $\binom{n}{k}$ ...
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1answer
107 views

Creating coexistent patterns, with several pattern-less systems

I'm a young musician, as well as a computer programmer. My understanding of math is formed well to my needs, but I am by no means a mathematician, but the field is very interesting to me. I have come ...
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1answer
306 views

Find the next number in this sequence

I have a homework. It seems to be an easy sequence but I can't get the answer. So, What is the next element? $$2, 7, 10, 13, 23, 34,?$$ What would be the solution out of these numbers? 45 or 49 or 58 ...
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2answers
107 views

Finding pattern (2,7,8,3,5)

What would replace $Z$ in the following sequencing? $$\begin{matrix} 2 & 3 & 4 \\ 7 & 6 & 5 \\ 8 & 7 & 1 \\ 3 & 0 & Z \\ 5 & ...
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1answer
97 views

A lemma regarding cones covering $\mathbb{R}^d$

Added: Pointers to some references with the same conclusion as the wolloing lemma may be helpful to understand it, and are appreciated. In A Probabilistic Theory of Pattern Recognition By Luc ...
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1answer
80 views

Game statistics: Extracting interesting patterns out of users and level

I made a small game and in course of time collected fair amount of data between users and level The level chart is long (120 levels) but looks somewhat like this $$ \begin{array}{|c|c|} ...
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1answer
74 views

Is there a pattern of the length between one even Fibonacci number and another?

I had seen a math problem asking for the sum of all even Fibonacci numbers up to 4 million, but I still need to know this: Is there an obvious pattern of the distance between a even Fibonacci number ...
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1answer
32 views

Generate random number based on a certain pattern and able to test against the pattern

I have very little idea about random numbers and patterns, so I am not sure whether this is actually possible or not. I want to generate random numbers, that will follow a fixed pattern (perhaps this ...
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5answers
65 views

How can I find the general formula for the following real sequence

How can I find the general formula for the following real sequence $$(x_n)_{n \ge0}=(1,0,-1,0,\frac{1}{2},0,\frac{-1}{6},0,\frac{1}{24},0,\frac{-1}{120},\ldots)$$ I just know $x_0$ to $x_{10}$ so how ...
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1answer
56 views

Determine Patterns

I have some weather data that I would like to analyze. I have about a millions rows of data, and each row has about 100 attribute values. Each attribute value represents some measurement (i.e., ...
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2answers
396 views

Logic of numerical series

One of our colleagues has written a numerical series to the whiteboard in our breakroom. Nobody until now could solve the logic behind this series: ...
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1answer
42 views

Anyone recognize this pattern? Plotting relationship between two parameters and their response.

First time asking a question here so hopefully I can provide enough information to you guys without explaining more than necessary. I'm doing some amateurish numerical analysis in MATLAB on some ...
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2answers
69 views

closed formula for a series

The first column below is n (iterator), the second is the value, I'm trying to understand if there is a closed formula that I can use for obtaining the value given a fixed n $$n=0: a$$ $$n=1: ...
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2answers
35 views

Equation for value of p given x

I have a set of numbers: $\begin{array}{r(22)}x \in \{ 1,& 2,& 3,& 4,& 5,& 6,& 7,& 8,& 9,& 10,& 11,& 12,& 13,& 14,& 15,& 16,& 17,& ...
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1answer
52 views

How can I figure out the total solutions in this Combinatorics problem?

Imagine you have a sequence of cards, each having a unique set of features. Example features : letter (A, B, C), number (1, 2, 3), and color (Red, Green, Blue) Some example cards : A1Red, B1Blue, ...
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25k views

I don't see the pattern.. does anyone understand this..? [duplicate]

Note.. the numbers are actually in a 7 x 6 grid.. graphics did not show here.. ...
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1answer
154 views

Find the pattern, what is the correct number in that spot, explain the answer

we are given the following matrix: $\begin{pmatrix} 9 & 38 & 47 &4 \\ 6 & 35 & 42 & ? \\ 12 & 21 & 23 & 27\end{pmatrix}$ The number that goes in $?$ is $-5$. I ...
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1answer
95 views

What makes a pattern in a sequence?

Assume a stream of characters$(c)$ where $ c \in (A, B, C ... Z)$. I need to identify patterns available in the stream. As per the definition of a pattern I should be looking for a recurring string. ...
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1answer
194 views

Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
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1answer
147 views

What is the pattern here? Q-function - SOLVED

I've got the following problem: The difinition of the funtion: Q(S,M). The purpose is to find the max number of possibilities how to write the funcition. ...
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1answer
64 views

Identifying a pattern in an array

Is there a way to identifying a pattern and/or recursive function for an array? If yes, how can I do this. Could anyone please help me with some information and/or resource for this? Any help is ...
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1answer
167 views

Finding the mean (or pattern) of a set of related values in a matrix discarding those that are too different.

this is my first question here so I am not sure if it is a valid one. I am currently facing a mathematical problem that is not so hard to solve, but given the accuracy i need in the results I would ...
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1answer
478 views

Equations and Pattern formulas problem solving

I have this question to answer and I need help with finding or creating a equation. You own a license plate manufacturing company. Write a formula or equation that takes a population and ...
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0answers
56 views

Is there a pattern that can be seen in this sequence?

I can't seem to find any pattern, perhaps a fresh view from one of you guys can point me to the right direction: 14898997873, 16483634594, 17241926510, 16427260053, 19933377255, 7467660818, ...
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0answers
14 views

Pattern recognition and machine learning - Bishop: Difficulty deriving (2.111) and (2.112)

I'm having a hard time deriving (2.111) and (2.112) in this book (it's on page 110/703). Here is what it says: Finally, we seek an expression for the conditionalp(x|y). Recall that the results for ...
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0answers
30 views

Solving a Recurrence for a Mathematical Game

The problem is: Two players take turns removing coins from a pile. There are initially $n$ coins, and on each turn, a player can remove $a_1, a_2, \dotsc, a_k$ coins. The player who cannot remove ...
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0answers
11 views

Frequency of a specific date, time, DoB combination/'palindrome'

Apologies if this isn't the correct forum to ask - I'm a regular Stack code user, this had me scratching my head for a while and just curious if someone a lot smarter than me can tell me how 'unique' ...
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0answers
15 views

Need help on Pattern problem

Hi I have problem on Pattern problem as shown picture. I can find only A B C butpending on D. Thanks. E.g. (First table) A = 7-1 =6 B = 7-6 =1 C = 7 + A = 7 + 6 ...
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1answer
25 views

What does this quantity measure?

Consider this list of numbers: $$\begin{bmatrix} 59 \\ 148 & 0.60 \\ 200 & 0.26 & 1 \\ 250 & 0.20 & 1.25 \\ 290 & 0.14 & 1.45 \\ 325 & 0.11 & 1.625 \\ 360 & ...
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2answers
36 views

Generate equation from pattern

What equation describes the growth pattern of this sequence: P = 5,25,35,55,65,85,95... Heres the diferences: 5 (20) 25 (10) 35 (20) 55 (10) 65 ... I have tried the P = Ax + B but it doesn work ...
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1answer
50 views

Pattern Finding in terms of previous terms

Find the next terms of the pattern: $$ 1,4,24,192,2120,31140,566202 \dots$$ Tell the pattern expression. I have already tried Lagrange interpolation. But it is not accurate enough.
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48 views

Why does this matematical pattern occurs here?

The actual question goes like this A room has N (1 to N inclusive) bulbs and N switches. N people go in one by one. 1st person goes in and toggles none of the switches. 2nd person goes in and ...
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0answers
8 views

Discriminant Functions of two classes sharing same covariance matrix

How can i find the discriminant functions of two classes having same diagonal covariance matrix with different means? (their feature vector is two dimensional) Thank you!
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0answers
12 views

Recognition rate prediction as a function of number of distractors

What would be a formula for extrapolating behavior of an algorithm that was tested with small number of false positives, say $10$ or $100$ but I want to know the rate with $1000$. E.g., the ...
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1answer
47 views

Hypersphere - Pattern matching using Centroid, Radius and Diameter

I have a hyper-sphere formed with set of $n$-dimensional data points. I could calculate centroid ($X_0$), radius($R$) and diameter($D$). Using these $X_0, R, D$, how I can find whether the a given ...
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0answers
52 views

In kernel rules, why is a regular kernel necessarily bounded?

Request from a dabbler in measure theory. Here a kernel merely designates a real-valued function. Quoted from "A Probabilistic Theory of Pattern Recognition", Luc Devroye, Laszlo Gyorfi, Gabor ...
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1answer
28 views

proof that a density proportional to Gaussian is Gaussian

I try to develop bayesian estimation for one dimensional Gaussian with unknown $\mu$ and known $\sigma$. I got $$p(x\mid D) = \int p(x\mid\mu)p(\mu\mid D) \, d\mu =\int \frac{1}{\sigma ...
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1answer
28 views

Trying to figure out a Mathematical pattern

I am given a start point, a, an end point b, and a number of values x. With that I am supposed to come up with the points between the start and end point. Below is an example ...
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0answers
30 views

Estimate prior for normal distributed data

I have successfully implemented a bayesian classifier using maximum likelihood. In my case I've got 2 classes and I have calculated the two $\mu$ and $\Sigma$. In my problem with a 3-dimensional ...
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1answer
60 views

how to calculate the marginal distribution of probabilistic principal component analysis

In the book Pattern recognition and machine learning from Bishop equation 12.33 states: $\mathbf{x} = \mathbf{W} \mathbf{z} + \boldsymbol\mu + \boldsymbol\epsilon$ Here $\mathbf{z}$ has a normal ...
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0answers
14 views

Is auto-correlation a particular and simple form of pattern in time series?

In a time serie context and considering the sign of the variation of the variable auto-correlation means that for couple of measures at (time t, time t+1) the ...