Automatic problem generation

Automatic Problem Generation

A new approach to Mathematical analysisPresented by: Abhishek Dey. Developer. Architect.

05/02/2023Prepared by: Abhishek Dey, Developer, Cloud Architect. 2

What is a problem?

▪ Take a typical example (Algebra):

is a quadratic equation. Resolve the factors.

Approach:1. We multiply a*c and resolve the common factors.2. We manipulate them and try to rearrange equation to satisfy

constraint b.3. where b’ is a constant.


Human Analysis Vs. Machine Analysis

Factorize a*c.

I. assume expr=a*cII. take a suitable integer x and

divide expr/xIII. if remainder is divisible by x,

continue (expr-x)/x else, check for a new divisor y (expr-x)/y.

IV. repeat unless expr reduces to a prime number or 1.


Computer’s Algorithm:

▪ Has to start from 2 and continue checking up to a*c-1 times.

▪ Iterator to – If , then

– Else

▪ Do you think this is smart ?


A better approach

▪ Fundamental Law of Arithmetic:– Every composite number can be expressed as a product of

primes.

▪ This makes the algorithm faster and smarter.

Number Number of Divisors

Prime 2Square of a prime 3Cube of a prime 4


Problem with Machines

▪ They generate random figures.– Can you solve ?– Probably. But not in a limited time.

▪ The generated problem may not have a unique solution.▪ Some problems such as Matrix Chain multiplication,

Bellman Ford, Dijkstra may require a lot of processing power.


Where there is will, there is a unique solution

▪ Processing Queue:– We use a distributed processing model.– Some problems from our end, others from customer’s

end.– We maintain a processing queue.– A worker role that keeps record of all the distributed

tasks going on.

Example:Say, we have a customer X who wants 10 questions on quadratic equations. The server supplies 5 of them and the remaining is generated in his system and backed up in our server.


Architecture of the back end

Backend Database

Processing QueueWrites data

Contacts tracker

We are Trackers! We keep track of

jobs


Determining a unique solution

▪ We form a Tree.▪ Trace all paths that can be

followed.▪ If we reach a wrong node, we

trace back using Backtracking.▪ Finally the correct path is

determined.▪ If the tree is too complex we

use Union-Find algorithm.▪ This also helps us to know the

difficulty level of a problem.


Another problem has come up!

▪ When a user chooses a level of difficulty for the generated problems, what do we mean by EASY or HARD?

▪ EASY is a relative term.▪ So, we employ 2 things:– A Machine Learning mechanism based

on sentiment analysis.– Feedback from live customers.

– What is MACHINE LEARNING?? :O


Achieved Throughput

500 1000 10,000 1,00,000 10,00,000 20,00,00005000000

10000000150000002000000025000000300000003500000040000000

No. of devicesNo. of devices

NO. OF DEVICES

No. O

F QU

ESTI

ONS


What’s the point?

We hate these situations!We want a solution. Maybe unique.


The UI and UX:

▪ Users will be offered:– Choose number of questions.– Choose difficulty level of questions.– If not satisfied with response, option to

discard question by just a slide.– The experience is sleek and hassle free.

▪ What we shall get:– We are Opensource. Not just FREE.– Entire profits from advertisements.– You contribute your processing power. (a

little bit.)– Build a platform for teachers.

To all the teachers, on Teacher’s Day

Thank You.

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Automatic problem generation

Software

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