**Long time, no blog**

Life’s been keeping me busy.

I’ll post

an update

soon.

Briefly: finished my summer job for the Amalgamated Insight

(née TelegraphCQ)

folks. I’m now back at Queen’s for the last year of my

undergrad.

**Interesting math**

An assignment in one of my

classes

included an

interesting

bonus problem. It is very simple, but I confess I got it

completely wrong before I saw the

solution. Maybe one of you bright folks is smarter than I:

Let the alphabet

A= {a, b, c, …, z} (Ais the

set of 26 lowercase letters of the English alphabet). Let

S1(w)be true iff the stringwover alphabet

Acontains the substringaaa; let

S2(w)be true iff the stringwcontains the

substringabc.

Suppose we choose a

w

of 10

characters; each

character inwis selected randomly and independently.

Let

P1be the probability

that

S1(w)

is true,

and letP2be the probability thatS2(w)is

true. IsP1 > P2,P1 < P2, orP1 =? Give a justification for your answer. (Hint:

P2P1).

!= P2

If you think you know the answer,

email me

—

I’ll post

the answer later (`neilc A T samurai D O T com`).

Obviously, the gist is in the

justification, not which alternative you think is true.

Hat Tip: Prof. Kai Salomaa

for showing me the problem.