Cake
• @apm please save us by explaining how he did this! đ¤Ż

• A maths diary

Higher maths problems are often about noticing patterns. So I started noticing patterns as I watched the video, pausing to jot down notes.

The performer is a mental magician. Â As a result, I start to notice a possible pattern of misdirection away from the fact that he has a British accent.

Relevant?

The two dice provide 36 possible unique numbers. Six possibilities for the first digit times six for the second digit.

Roll a 1 for the first die and you have 6 possible numbers: 11, 12, 13, 14, 15, 16.

Same for rolling a 2,3,4,5 or 6 with the first die.

So six sets of six or 36

[BEGIN Off-tangent aside]

It helps when problem solving to notice interesting math facts and questions that come to mind. Â Your questions may lead to an even more interesting math problem to solve.

I wonder what the possible sums are of the two numbers rolled and how many times each sum occurs:

Sum of 2. Â Occurs once. 11

Sum of 3. Â Occurs twice. 12, 21

Sum of 4. Â Occurs thrice. Â 13, 31, 22

Interesting question: Can you predict how many times the sum of 6 occurs just by studying the above pattern? Â How about if you had three dice?

[END of Off-topic aside]

Collin takes the dice and rolls a 33

then 62

then 45

The magician breaks down the last number first. Â Why? Whatâs special about 45?

He breaks it into 10, 17, 10 and 8.

Why those numbers and why four numbers?

He breaks 45 into four different numbers: 3, 5, 15, 22.

One of the problem solving techniques in maths is to try to solve a smaller problem first. Â I have no idea at this point what heâs going to do or say next, but I want to take a moment to notice if thereâs any pattern or reason for breaking 45 by these two ways.

Other than noticing three prime numbers in the mix, I donât notice anything useful.

[BEGIN Off-topic aside]

@Felicity mentioned the challenge of not having short content to publish when youâre knee deep in writing a novel. Â Hereâs a 500 character writing prompt, a Maths short story, that I crafted on Mastodon, tweeted on Twitter, and then immortalized on Threader.

âWhen will we ever use this?â

(A short story)

[END of Off-topic aside]

The performer breaks 45 down two more times, so four different breakdowns.

10, 17, 10, 8

3, 5, 15, 22

13, 13, 12, 7

19, 0, 18, 8

I pause the video.

Remember when I said he was a magician and prone to misdirection? Â Why did he pick 45 to play with, instead of 33 or 62? Why is the same number used twice in both the first and third breakdowns? Â

Why do I feel that heâs intentionally focused my mind on these red herrings so that I miss the key to whatever the impending trick is?

Okay, I finally get to the trick of the numbers turning into a 4x4 matrix where, like Suduko, each row and column sums to 45. Â

The fact that he can mentally create this matrix for any number is insane, but itâs not outside the realm of human capabilities. Â Daniel Tanner, an âAutistic Savant,â can rattle off Pi to 22,500 places and learned to speak Icelandic fluently in seven days.

But how did the magician get the hostâs birthday to appear on the last line of the matrix?

The only logical answer is that he knew multiple important dates to choose from should the three numbers rolled be different: his anniversary, his wifeâs birthday.

Interesting maths question: how many dates would the magician need to know to cover every unique combination of three rolls? Â i.e., rolling 33-62-45 is the same as rolling 45-62-33.

It probably took an insane amount of time to prepare for this trick, but Jerry Seinfeld says that he usually spent twenty or more hours preparing for the Tonight Show.

• I was actually even more impressed by his ability to pick an exact number of grains than by his ability to remember up to 36 different and probably pre-calculated number squares - but watching that part again, I think it's the key to understanding the whole sequence:

At around 6:25 in the video, he picks up a pencil with his right hand and seems to put it away into his pocket. This action itself is not visible in the video - but starting at 6:32, you'll notice that his hand is now clenched to a fist. He then pretends to pick some rice with three fingers, but probably doesn't and instead pours the rice he already held between palm and remaining two fingers onto the table.

If this is the case, then either he must have had a way to get any number of grains of rice (11, 12, ..., 66) from his pockets, or some combination where maybe he is skilled enough to quickly pick between 0 and 3 grains of rice and then he combines it with one of nine different prepared heaps - or he simply had 45 grains in his pocket because he already knew that this is the number that would be used.

Considering that it might be hard to find 36 different dates (or other number sequences) that don't seem too contrived to spontaneously bring up, each of which adds up to a different number from the set of possible dice rolls, I think it is likely to assume that he did mess with the dice rolls after all, to get the result he wanted - so let's have another look at that part of the video, starting at around 3:00:

One thing I notice is that he picks up the glass bowl containing the dice an awful lot - and in fact, following just the bowl, you'll notice that he sets it down in a different place for the first two rolls (along the side of the board) than for the last roll (near the edge of the board). Looking at just the final dice roll, it also looks as if the dice behave a little different and "click" into place faster than the two times before. I guess that there's a magnet hidden under the board, and that this is how he ensures the result of 45 to use in the rest of the trick.

• I think you're on the right path. After all, he's billed as an illusionist.

My guess.

He researched Corden's b-day and built that matrix. Then memorized it.

The dice were "loaded." He did decisively put the bowl in a difference place. A magnet makes sense.

Then he goes the through the dog and pony show.

Because he already knows that 45 is his number, he has 45 grains of rice stashed up his right sleeve.

If you watch, you can see his palm change shape and eventually turn into a clenched fist. That's when the grains fall into his hand. He then make an awkward pretense of scooping grains and putting them on the table. Everything about those two motions looks unnatural.

He's a Pen and Teller kind of guy.

• Iâve seen most of Penn and Tellers TV specials over the years, including the illusionists competition last summer. It is always about the story that misdirects you. The illusionist couldâve failed high school maths, but he makes you believe that heâs a math savant within the first two minutes.

Note: My previous post above couldâve been cut to two paragraphs on the misdirections and memorizations required, however, in fairness I didnât want @Chris or myself to get reprimanded for using the mathematics topic in what is obviously a conversation about magic!

đđ¤Ł

• Hahaha, okay I added entertainment as a topic. We don't have magic yet.

But wait. Is this math or magic?

• If you never struggled with mathematics, then you will be of little use in teaching mathematics because you will have zero experience of the fundamental idea of learning mathematics. Sunil Singh

Problem solving strategies used:

1) Identify the type of problem youâre dealing with, especially if there are type-specific strategies for solving

2) Make the problem simpler

Identify the type of problem:

This appears at first glance to be a âGuess your numberâ demonstration where you add and multiply different numbers to your number and then divide and subtract to get back to your original.

The misdirection will be the need to use a calculator so that you donât explicitly see the math. Which leads to

Make the problem simpler:

We could pick an easier number to use, such as 10 or 100, to avoid the need for a calculator. An even better strategy is to use Algebra and substitute with a letter.

Step 1: Pick a number between 1 and 9

Result: Let n = my number

Step 2: Multiply by 2

Result: 2n

Result: 2n + 5

Step 4: Multiply by 50

Result: (2n+5)*50

= 100n + 250

Result: 100n+250 + 1767

= 100n + 2017

Step 6: Subtract your birth year (Iâll use 1985)

Result: 100n+2017-1985

We cracked the code!!!

The first digit of the resulting 3-digit number will ALWAYS be your original number.

The puzzle video was apparently introduced in 2017. For 2018, you would add 1768 in Step 5.

• I ought to be the world's finest math teacher, then.

• Welcome to Cake, Drew. đ

• Hey Drew! Like your grand entrance.

@Chris has provided instructions on how weâll join in the panel on Saturday: basically, after I create the panel session, Cake will email you a link to join in.

Hereâs a link to what it will look like. If you have any questions on the set up, how to format your thoughts if you want to get fancy, etc., you can click reply to Chrisâs post below, ask away and someone from Cake will respond to help us out.

• For those not involved in the maths education universe on Twitter, Drew is an amazing mathematician, educator and recreational maths puzzle expert. Heâs been involved in multiple online learning platforms including learningclip.co, which he co-created, and Maths-Whizz. Drewâs recreational maths puzzles on Twitter are regularly enjoyed by maths educators and their students. He is a frequent presenter at maths conferences throughout the UK.

Iâve been a big fan of Drewâs recreational maths since I discovered them this summer and am thrilled that he will be participating in Saturdayâs panel on âHow do you make maths fun?â

• Thank you apm, youâve been incredibly kindđ

• Nice, Drew. If only there were more people like you in the world.

• Dan's popular TEDx talk. Loved it.

• I will do the same as we get closer to the time.

• I love that I have this memory of me teaching my class. I think this was for TeachersTV, my students loved the experience.

I had developed and written all the digital content as well as working full time.

• Response from @drewfoster via Twitter. âŹď¸

@gorudy I believe the correct math term for this self-reference is called recursion.