But what are the chances of getting 10 heads in a row? Fairly low, right? (how low I’ve no idea). So if I do 9 consecutive coin tosses and each time I get a head, surely that means the odds of the 10th coin toss being a HEAD are pretty low and of being a TAIL have dramatically increased beyond 50%?

When you look at the toss in isolation it’s 50/50 but when taken as part of a series, do the preceding results have bearing on the outcome of the next throw?

Dan plz explain.

"She needed to perform one more vault,
She needed to sprint down the runway, jump off the springboard, fly spinning through the air…and stick the landing.
And she needed to do it all on one foot. "

They are referring to Keri Strug’s vault as part of the 1996 Games.

Unfortunately the entire ad is based on a false premise. Not taking anything away from Strug’s achievement but I’m sure she herself realizes by now that based on the scores at the time, if Keri’s coaches had been able to perform the basic arithmetic in their heads they would have realized that in fact she DIDn’t need to perform that vault.

From Wikipedia: "Strug under-rotated the landing of her first attempt, causing her to fall and damage her ankle. Despite this, the attempt was awarded 9.162 points…the American coaches were unable to compute "quickly enough" whether a second vault was necessary."

"In the excitement of the moment, I think they forgot how to add. I was wondering why she went again. I thought, Gosh, that’s brave when she really doesn’t have to do it."
—Jackie Fie, international gymnastics official at the table in Atlanta

If Visa had done their research, they would have probably worded this ad differently. This is also a great example of the human response to authority figures. Great moment all the same.

I came across IBM’s website on burr puzzles [LINK] and decided to make one.

"Burr puzzles are interlocking puzzles known in Europe and Asia since at least the 18th century. Traditionally they are made from wood….and require special wood so that the pieces do not change shape too much in changing temperature and humidity."

Burrs? You had me at "35.65 billion".

I first picked "David Winkler’s favorite level 5 burr" [LINK]. This is a "notchable" burr meaning you can construct it entirely by notching the pieces. I used a bit of red-oak I had laying around. This burr is 6 units long, 2 wide. The unit size in my case is 3/8" which I found a good size. The design in this case is a "5.4" meaning there are 5 moves required to remove the first piece, then 4 to remove the 2nd.

My kids got a good kick out of this one and they’ll likely play with it in years to come. Sunday night I caught the bug again and decided to make another. This time a "general" design meaning one where the pieces are not just notched but also have some partial voids. Slightly more complex to create but allows for more complex solution. I decided to go all out and chose Peter Marineau’s
Piston Puzzle Burr [LINK].

"1986: Peter Marineau designed this puzzle by hand. It was the highest level burr known before Bill Cutler did his exhaustive computer analysis."

I made this one out of cherry with its tighter grain and the fit is a lot better, mostly due to me taking my time. The action in Marineau’s is such that the first piece only comes out after a full 9 moves then 3 more for the 2nd piece. So cool.

I imagine this is the type of puzzle my grandfather would have enjoyed making if he had had the same resources available as me. The chisel remains the most dangerous tool in my shop.

For the next two months, my kids ages mimic my own age’s digits.
This will not happen again in my lifetime.

In 26 years my kids ages added together will equal my age.

How old am I and how old are my kids?

Dan [LINK] would get a kick out of this.

Dan’s claim to fame is his ability to recite Pi to the 20th decimal, so imagine how quick he was to point out the error in a recent photo taken of a sculpture taken at the Oregon Zoo. Here’s the photo.

Poor Dan so quick to judge thought that the artist’s sole intention was to list Pi in a square format. He quickly noticed however that the numbers are not correct and assumed an error on the part of the un-educated artist.

I looked a little deeper and discovered that these are in fact portions of pi from the first 1000 digits. After 10 mins examining the numbers I came up with the following:

So clearly there is NO error on the artist’s part and in fact there is a pattern to the numbers. It would appear the square is divide diagonally. The first 10 digits of the 2nd line match Pi at position 102. Eight of the next row’s numbers match Pi at position 204 and this continues up until the 6th row. 62 actually matches in a few places but following the pattern is also matches at position 510.

Interestingly there are nine rows total. Rows 7, 8 and 9 also match but the pattern starts over. The first 10 digits of row 7 match at position 702, a break in the previous sequence of 102, 204, 306, 408 etc.

Again 10 digits from row 7, then 8 digits of row 8 and finally 6 digits of row 9.

Then taking the numbers that were left over from the rows, starting with row 2, 44 matches at position 202. 7245 matches at position 302. So another sequence is revealed there. There’s a break at position 702 though. Maybe that’s because position 702 was already matched at row 7?

I tried one other thing this morning which is to re-arrage ALL the numbers into rows of 10 instead of 12. This yields much better results.

This still leaves some digits left-over, namely 897932.

At least this proves the artist was not foolish enough to carve random numbers into the rock hoping no one would question that they’re Pi. And more importantly it also gave me a rare chance to stick it to Dan How’s the pie Dan?

"A dozen, a gross, and a score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Is nine squared and not a bit more."

(12 + 144 + 20 + 3sqrt(4)) / 7 + 5*11 = 9^2

The second is a thing called Tupper’s Self-Referential Formula. This is a formula (displayed on the page linked below) that when plotted on a graph, draws a picture of….ITSELF!!!

It’s just one of those one in a million flukes but weird nonetheless: [LINK].

"Just like that flat lander who can only see two dimensional cross sections of objects from the dimension above, we as three dimensional creatures can only see three dimensional cross sections of our fourth dimensional selves."

And I’ve gone cross-eyed.

Here’s a breakdown:

• 1st dimension – joining two points – a single line
• 2nd dimension – Three points – a single plane
• 3rd – Two intersecting planes – Where we live
• 4th – Us + time
• 5th – Us + time + choice, "the subatomic particles that make up our world are collapsed from waves of probabilities simply by the act of observation" – (I’m so glad I read Schroedinger’s Cat)
• 6th – Folding the 5th through the six to jump to a potential new position in the 5th dimension. Not time travel but a "dimensional jump".
• 7th – All possible time lines which could have or would have occurred, ever: Infinity.
• 8th – Joining two different infinities (like 2Dimensions).
• 9th – folding the 8th – traveling through entirely different infinities.
• 10th- All possibilities are contained herein. This is where Strings live.

Ok, so it kind of lost me at the 10th but the 1 through 9 made pretty good sense.