ThinkingNectar

I spend a good hour reading a Martin Gardner book over the last weekend. I will say it kept the mind occupied and it is always good to revisit some books that you had read when you were younger. If my memory does not fail me, the first time that I touched Gardner’s book was when I am 17. Pretty late I will say.

The current book have 2 rather interesting parts which I like to share. Those who knows me well enough will uunderstand that I do have a keen interest in understanding how and why human make mistake, or mis-judgement.

The ten travellers

Ten weary footsore travelers,
All in a woeful plight,
Sought shelter at a wayside inn,
One dark and stormy night.

“Nine rooms, no more,” the landlord said,
“Have I to offer you.
To each of eight a single bed,
But the ninth must serve for two.”

A din aroise, The troubled host
Could only scratch his head,
For those tired men no two
Would occupy one bed.

The puzzled host was soon at ease–
He was a clever man–
And so to please his guestes devised
This most ingenious plan.

In room marked A two men were placed,
The third was lodged in B,
The fourth to C was then assigned,
The fifth retired to D.

In E he sixth he tucked away,
In F the seventh man,
The eighth and ninth in G and H,
And then to A he ran,

Where in the host, as I have said,
Had laid two travelers by;
Then taking one– the tenth and last–
He lodged him safe in I.

Nine single rooms– a room for each–
Were made to serve for ten;
And this is that puzzles me
And many wiser men.

It got me the first time. Seems on the first count that some how the inn keeper threw the pigeonhole principle out of the window.

For part 2, we have a simple maths equation.

a = b +c

Multiply both sides by a-b to obtain:

a² – ab = ab + ac – b² – bc

Move ac to the left side:

a² – ab – ac = ab – b² – bc

Factor:

a ( a – b – c ) = b ( a – b – c)

Divide each side by a-b-c to get:

a = b

Again, find how where is it that your mind got lead astray.