Wednesday, December 26, 2007


Here's an innovative CAPTCHA I came across when trying to register for a forum at

You have to enter resistance between A and B in the diagram below. Can you do it?


Anonymous said...

3 Kirhoff laws is all you need.
Странно, в мое школьное время (начало 80-х) такие задачки
были хлебом в 9-м и 10-м классе мат-школ. Чего такого заслуживающего в ней??

Yaroslav Bulatov said...

Чего заслуживающего в этой задаче будет ясно из следующего поста :)

Stephen said...

Interesting. Seems like they are filtering more than just spambots.

Yaroslav Bulatov said...

True, the CAPTCHA is probably there to filter out those pesky mathematicians, botanists and other non-physicists.

You can derive it directly from 2 Kirchhoff's laws (voltage around every loop is 0, net current at every node is 0), but it gets a bit messy. section 2.1 of Bollobas' "Modern Graph Theory" works out a simple example in detail using this method.

Most practical method is probably to use a CAS and a formula for 2-point resistance of general graphs (formula 2 of, also see for derivation

Without CAS, you could use parallel (conductances add), series (resistances add) and star-triangle laws (see Bollobas 2.1) to simplify the network into a single resistor

There are some interesting connections between theory of resistor networks and partition functions of statistical models. Alan Sokal (same one as the Alan Sokal hoax)
shows that partition function of Potts model has equivalents of parallel/resistance laws of electrical networks

Also, there's a 1-1 correspondence between electrical networks and reversible Markov chains (ie,, so you could potentially use theory of Markov Chains to solve this problem as well

L. Venkata Subramaniam said...

Do you think one day the author of this forum will not be able to solve the circuit theory problem and hence be unable to enter?

I am speculating that he will forget to solve it soon after his 80th birthday. I hear thats when the resistance of the neuron sheaths breaks down and the charge carrying capacity comes down drastically.

Sports education worldwide said...

nice post thanks for sharing
appvn apk
tutuapp apk ios

john said...

Great Article
IEEE final year projects on machine learning

JavaScript Training in Chennai

Final Year Project Centers in Chennai

JavaScript Training in Chennai

Essay Help said...

Your blogs are authentic. I love them .Are you also searching for essay help? we are the best solution for you. We are best known for delivering quality essay help.

cheap assignment writing help said...

I love this. It is soo informative. Are you also searching for cheap assignment writing help we are the best solution for you. We are best known for delivering the best services to students without having to break the bank

periyannan said...

This is the first & best article to make me satisfied by presenting good content. I feel so happy and delighted. Thank you so much for this article.
ibm full form in india |
ssb ka full form |
what is the full form of dp |
full form of brics |
gnm nursing full form |
full form of bce |
full form of php |
bhim full form |
nota full form in india |
apec full form |