Puzzle: What's my birthday?

I was lucky enough to attend a 'Let's Talk Oracle' session from Canberran Richard Foote today diving into AWR.

After an early dad joke and before we got into his AWR collection, we gave this brain teaser.

Screw you, logic puzzle. I came so close #logic pic.twitter.com/oAcMiXPRCo

— Scott Wesley (@swesley_perth) May 5, 2016

This hurt many heads, including mine, and I also picked the wrong answer. Richard reports our group did well though, compared to other cities. Nice work to the Twitter peeps that also gave this a go.

My very first pass got me to July 18, but let the brain simmer a little further and you realise the rabbit hole is longer than expected.

Then I arrived at July 16 because I wasn't scribbling anywhere and my brain obviously couldn't plan enough moves ahead. The answer slapped me in the face soon after Richard crossed out May. I eliminated 18 and 19 and thought there was a nice looking date sitting by itself.

I knew a friend would eat this up and he vehemently concluded the answer was Aug 16, so I just had to break it down so I could send him my working.

Spoiler alert: the true answer appears at the end of this post.

***

Bowie and Ziggy see this list

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

Bowie told Month
Ziggy told Day

Fair presumption: Each other knows they only know a portion, because Bowie states Ziggy doesn't know both pieces of information.

If May, there is potential Ziggy knows unique number, so Bowie couldn't be certain Ziggy doesn't know.

If June, days are non-unique, so Bowies knows Ziggy couldn't be certain either way.

If July, same possibility as May

If August, same uncertainty as June.

So from Bowie's perspective, we are left with these possibilities, those months with unique numbers

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

Ziggy states at first he didn't know, so unique numbers can be eliminated.

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

All other days have duplicate, so Ziggy still uncertain of month.

Now Ziggy knows Bowie was uncertain with just month, Ziggy shares that knowledge and eliminates same months.

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

It's down to three uniques, because Ziggy states he now knows, and 14 is not unique.

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

Now Bowie says he also knows. He still can't tell between the two August days

May 13	May 15	May 19
June 13	June 14
July 16	July 18
August 14	August 15	August 16

June 13 must be the answer.

Richard's explanation

https://richardfoote.wordpress.com/2015/04/23/singapore-maths-question-solution-and-very-interesting-observation-the-trickster/

When the question went through the media rounds

http://www.smh.com.au/world/the-solution-to-the-teenage-maths-question-that-has-stumped-the-world-20150414-1mkioy.html

Ouch.