## 8-grid challenge

Put the numbers 1-8 in the grid such that no two consecutive digits touch each other horizontally, vertically or diagonally.

<pre>&nbsp; +---+---+
&nbsp; | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
&nbsp; | | |
&nbsp; +---+---+</pre>

<details>
 <summary>Solution</summary><pre>&nbsp; +---+---+
&nbsp; | 3 | 5 |
+---+---+---+---+
| 7 | 1 | 8 | 2 |
+---+---+---+---+
&nbsp; | 4 | 6 |
&nbsp; +---+---+</pre>
</details>

## Three of each digit

For each digit from 0 to 9, use exactly three copies of that digit (and any valid arithmetic operations) to create an expression that evaluates to 6.

<details>
 <summary>Solution</summary>$$(0!+0!+0!)! = $$ 
$$(1+1+1)! = $$ 
$$2+2+2 = $$ 
$$3*3-3 = $$ 
$$\sqrt{4}+\sqrt{4}+\sqrt{4} = $$ 
$$5/5+5 = $$ 
$$6+6-6 = $$ 
$$7-7/7 = $$ 
$$(\sqrt[3]{8}+8/8)! = $$ 
$$\sqrt{9}*\sqrt{9}-\sqrt{9}) = 6$$
</details>

## Soma cube solution

![Soma cube solution](/img/notes/soma-cube-solution.svg)

Misc puzzles

[Top]

8-grid challenge

Three of each digit

Soma cube solution

## Si Stebbins stack

[[\*](https://www.youtube.com/watch?v=TdTFweigAF4), [\*](https://www.youtube.com/watch?v=6b_Pl7HhdJk)]

The **Si Stebbins stack** is a cyclic mathematical card stack in which each card alternates suit in the **CHaSeD order** (Clubs Hearts Spades Diamonds), and has a numerical value **three** greater than the preceding card (A&clubs;, 4&hearts;, 7&spades;, 10&diams;, K&clubs; ... 8&spades;, J&diams;).

Since the bottom card of the deck is in order with the top card making an endlessly repeating cycle, it can be cut (not shuffled) any number of times without disturbing the order.

The following mathematical formula can be used to determine the value and suit of a card at any position in a Si Stebbins deck.

- Value of $n$th card $(V_{n}) = (V_{b}+3n)\mod13$
- Suit of $n$th card $(S_{n}) = (S_{b}+n)\mod4$

Where,

- $V_{b} =$ Value of bottom card,
- $S_{b} =$ Suit of bottom card (1 for Clubs, 2 for Hearts, 3 for Spades, 0 for Diamonds)

The position of a card with suit $S_{n}$ and value $V_{n}$ is given by:

$$
n = 13(S_{n}-5) - 4(V_{n}-V_{b})\mod52
$$

## Fitch Cheney's Five Card Trick

### Effect

This is 2 person trick. A spectator chooses 5 random cards from a shuffled deck. Person A (the "assistant") shuffles the 5 cards in a seemingly random order, flips 1 of them down, and hands over the 4 face up cards to Person B (the "mind reader"). Person B successfully tells what the face down card is.

### Method

From the [pigeonhole principle](https://en.wikipedia.org/wiki/Pigeonhole_principle), it follows that at least 2 out of the 5 chosen cards must have the **same** suit. The assistant chooses the "larger" one to be the hidden card and flips it down. The "smaller" one becomes the first card in the collection of 4 cards that person B gets. Person B looks at this card to determine the suit of the hidden card.

The rule that determines the "larger" card is as follows: imagine the 13 cards of a particular suit like the hours in a clock with 13 numbers (Ace = 1, Jack = 11, Queen = 12, King = 13). Any 2 numbers in this clock ([cyclic order](https://en.wikipedia.org/wiki/Cyclic_order)) are at most 6 steps apart, for example, 7 is 6 steps ahead of 1, 1 is 5 steps ahead of 9, and so on. The larger card is the one that comes second in this sense. For example, we should assume 2&hearts; is larger than 10&hearts;.

In other words, if the difference between the ranks is $\gt 6$, the "larger" card is the one with the smaller rank.

![13 clock](/img/notes/excalidraw/13-cyclic-order.svg)

To convey the rank of the hidden card, the assistant uses the 3 remaining cards by ordering them in one of $3! = 6$ ways indicating the hidden card is that many steps ahead of the first card. The order is determined by the **CHaSeD rule** (Clubs Hearts Spades Diamonds).

\*L = Low, M = Middle, H = High

- LMH -> +1
- LHM -> +2
- MLH -> +3
- MHL -> +4
- HLM -> +5
- HML -> +6

### Example

Suppose the spectator chooses 3&spades;, 7&clubs;, 7&diams;, Q&spades; and 3&hearts;.

1. Repeating suit is &spades;.
2. 3&spades; is 4 steps ahead of Q&spades;. 3&spades; becomes the hidden card. Q&spades; becomes the first card.
3. To denote the number 4, the remaining cards must be ordered in MHL format.
4. Person A hands over the cards to Person B in this order: Q&spades;, 7&clubs;, 7&diams;, 3&hearts;

## Water and wine

[[\*](https://www.youtube.com/watch?v=aqKkwTKWWUQ), [\*](https://www.youtube.com/watch?v=99R7UiJAg6w)]

### Effect

From a randomly shuffled deck of cards, 20 of them face-up and 32 face-down, the spectator hands out 20 randomly chosen cards to the magician and keeps the rest to themselves. The performer then (without seeing the cards) rearranges their own cards so that the number of face-up cards they hold matches the number of face-up cards the spectator has.

### Method

The "rearrangement" is done simply by flipping the deck of cards the performer has. Since this is a self-working trick, it can even be done blindfolded to prevent counting or tracking.

## Whispering Jokers

[[\*](https://www.youtube.com/watch?v=vKxFzSwcOhY)]

- Take a deck of cards and put two jokers J1 and J2 at positions 10 and 29 respectively.
- Cut the deck about 1/3rd of the way down. The bottom card is the chosen card X. Cut the remaining deck half-way down. The bottom card is the chosen card Y. 
 In other words, cut the deck at points X and Y such that 10 < X < Y < 29. Separate the deck into 3 piles (1 through X, X+1 through Y, and Y+1 through 54).
- Put `Pile1` on top of `Pile3`, then put `Pile2` on top of the rest.
- Split and remove the jokers. Separate the deck into 3 piles.
- Put `Pile3` on top of `Pile2` and then `Pile1` on top of the rest.
- The 18th and the 43rd cards from the top of this deck will be the chosen cards X and Y respectively.

## Misc

- [Kruskal Count](https://en.wikipedia.org/wiki/Martin_David_Kruskal#Kruskal_Count) [[\*](https://www.youtube.com/watch?v=yeJD98Zrmu4), [\*](https://www.singingbanana.com/Kruskal.pdf)]
- [Trick deck](https://en.wikipedia.org/wiki/Trick_deck)
 - Marked deck [[\*](https://www.youtube.com/watch?v=L8GsxU6Zt0E)]
- [False shuffles](https://en.wikipedia.org/wiki/Shuffling#Faking)
- [False cuts](<https://en.wikipedia.org/wiki/Cut_(cards)#False_cut>)
- [Numbery Card Trick - Numberphile](https://www.youtube.com/watch?v=dHzUQnRjbuM)
- [Magic 13 - Vsauce](https://www.youtube.com/watch?v=rUW_i5ucA9g)

Card tricks

This is a collection of some mnemonics that I discovered on the internet or have come up with myself. I only use a portion of these right now&mdash;some are classics whereas others are included for completeness.

Mnemonics that I've shared on the weblog:

- <Link href="/weblog/us-states">Mnemonic for US states</Link>

## Major system

[[Wikipedia](https://en.wikipedia.org/wiki/Mnemonic_major_system)]

| Numeral | Associated letters | Mnemonic |
|---------|--------------------|----------------------------|
| 1 | t, d | t, d have 1 downstrokes |
| 2 | n | n has 2 downstrokes |
| 3 | m | m has 3 downstrokes |
| 4 | r | Four ends with r |
| 5 | l | Roman numeral L equals 50 |
| 6 | j, sh, ch, soft g | Uppercase G looks like a 6 |
| 7 | k, hard g, hard c | 7 is angular like the k |
| 8 | f, v, ph | Cursive f looks like an 8 |
| 9 | p, b | 9 looks like a backward p |
| 0 | z, s, soft c | Zero begins with z |

The consonant sounds of **h**, **w**, and **y** can be added freely since they don’t appear on the list. For example, 32 can become man, human, woman, or Yemen.

## Morse code

[[Wikipedia](https://en.wikipedia.org/wiki/Morse_code_mnemonics#English), [Vsauce video](https://www.youtube.com/watch?v=HY_OIwideLg)]

### Numerals

| Numeral | Morse code |
| ------- | ---------- |
| 1 | • - - - - |
| 2 | • • - - - |
| 3 | • • • - - |
| 4 | • • • • - |
| 5 | • • • • • |
| 6 | - • • • • |
| 7 | - - • • • |
| 8 | - - - • • |
| 9 | - - - - • |
| 0 | - - - - - |

### Alphabets

Note: In word mnemonics, short letters (aceimnorsuvwxz) correspond to a dot and tall letters (bdfghjklpqty) or uppercase letters correspond to a dash. These are taken from [Douglas Harder](https://ece.uwaterloo.ca/~dwharder/Morse_code/files/Morse_code.pdf).

\*: Tall letters with morse code starting with a dot.

| Alphabet | Morse code | Syllabic mnemonic | Word mnemonic |
|-----------|------------|---------------------|------------------------|
| Aa | • - | aPART | at |
| Bb | - • • • | BOOT to the head | beer |
| Cc | - • - • | CO-ca CO-la | Cate (name) |
| Dd | - • • | DOCK WORK-er | dam |
| Ee | • | eh? | e |
| Ff | • • - • | get a HAIR-cut | cafe* |
| Gg | - - • | GOOD GRAV-y | gym |
| Hh | • • • • | hip-pi-ty hop | ears* |
| Ii | • • | i-i | in |
| Jj | • - - - | lets JUMP JUMP JUMP | edgy* |
| Kk | - • - | KAN-ga-ROO | kit |
| Ll | • - • • | he LOST his lid | else* |
| Mm | - - | MMMM-MMMM | MM (2000) |
| Nn | - • | NA-vy | No! |
| Oo | - - - | ONE OF US | IOU |
| Pp | • - - • | a POO-py smell | apps* |
| Qq | - - • - | GOD SAVE the QUEEN | plaq* |
| Rr | • - • | ro-TA-tion | rye/rho |
| Ss | • • • | si-si-si | six |
| Tt | - | TALL | t |
| Uu | • • - | un-der-WHERE?! | ump |
| Vv | • • • - | Beet-ho-ven's FIFTH | vent |
| Ww | • - - | a WHITE WHALE | why? |
| Xx | - • • - | X marks the SPOT | foxy* |
| Yy | - • - - | WHY did I DIE? | yell |
| Zz | - - • • | ZINC ZOO-keep-er | Zhou (Chinese dynasty) |

### Characters

| Character | Morse code | Syllabic mnemonic | Word mnemonic |
|-----------|---------------|----------------------------|---------------|
| . | • - • - • - | a STOP a STOP a STOP | stop it |
| , | - - • • - - | COM-MA, it's a COM-MA | plough |
| ? | • • - - • • | it's a QUESTION, is it? | and how |
| : | - - - • • • | HA-WA-II stan-dard time | pylons |
| / | - • • - • | SHAVE and a HAIR-cut | knife (slash) |
| " | • - • • - • | six-TY-six nine-TY-nine | a quote |
| ' | • - - - - • | and THIS STUFF GOES TO me! | rhythm |
| ; | - • - • - • | A-list, B-list, C-list | dododo |
| ! | - • - • - - | | to yell |
| ( | - • - - • | | hedge |
| ) | - • - - • - | | hedged |
| + | • - • - • | | clubs |
| - | - • • • • - | | barrel |
| = | - • • • - | | level |
| _ | • • - - • - | | so flat |
| & | • - • • • | | again |
| @ | • - - • - • | | at Fiji |
| $ | • • • - • • - | | richest |

## CS and Programming

- OSI Network Layer model (Physical, Datalink, Network, Transport, Session, Presentation, Application):

 **Please Do Not Throw Sausage Pizza Away** 
 **Please Do Not Teach Students Pointless Acronyms**

- CSS margin: **TRouBLe** (Top Right Bottom Left)

 ```css
 .class {
 margin: T R B L 
 }
 ```

## Math

- Order of Operations (Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction):

 **PEMDAS**

- Euler's characteristic (X = F + V - E):

 **fav.me** (F add V, minus E)

- Trigonometric ratios (Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent):

 **SOH CAH TOA**

- Determining which functions are to be chosen as u and DV in integration by parts (Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential):

 **LIATE**

- Sign of each trigonometric functions in each quadrant of the plane: **All Students Take Calculus** or **ASTC**
 - Quadrant I: All trigonometric functions are positive.
 - Quadrant II: Sine and cosecant functions are positive.
 - Quadrant III: Tangent and cotangent functions are positive.
 - Quadrant IV: Cosine and secant functions are positive.

- e (2.718281828459045)
 - Andrew Jackson was the 7th president of the US: 7
 - He was elected in 1828 and served two terms: 1828 1828
 - His favorite type of triangle was the right angled isosceles triangle: 45 90 45

## Science

- Order of planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto):

 **My Very Easy Method Just Speeds Up Naming Planets** 
 For eight planets: **My Very Easy Memory Jingle Seems Useless Now**

- Colors of rainbow (Red, Orange, Yellow, Green, Blue, Indigo, Violet):

 **ROYGBIV** (**VIBGYOR** in reverse)

- Layers of atmosphere (Troposphere, Stratosphere, Mesosphere, Thermosphere, Exosphere):

 **The Strong Man's Triceps Exploded** 
 **The Sick Man's Thermometer Exploded**

- Diatomic elements (Bromine, Iodine, Nitrogen, Chlorine, Hydrogen, Oxygen, Fluorine):

 **BrINClHOF** (pronounced 'brinkelhoff')

- **PANIC**: Positive Anode Negative Is Cathode.
- **LEO the lion says GER**: **L**oss of **E**lectrons, **O**xidation; **G**ain of **E**lectrons, **R**eduction
- **AN OIL CAT RIG**

 At the **AN**ode, **O**xidation **I**nvolves electron **L**oss. 
 At the **CAT**hode, **R**eduction **I**nvolves electron **G**ain.

- Speed of light (299,792,458):

 **nabob cabin relief** (Major system) 
 **We guarantee certainty, clearly referring to this light mnemonic** (Counting the number of letters in each word)

- Increasing frequency or decreasing wavelength of electromagnetic waves (Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-Rays, Gamma Rays):

 **Rich Men In Vegas Use eXpensive Gadgets** 
 Opposite order: **Good Xylophones Use Very Interesting Musical Rhythms**

- Order of taxa in biology (Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species, [Variety]):

 **Dear King Philip Came Over For Good Soup**.

- Resistor color codes: **Better Be Right Or Your Great Big Vacation Goes Wrong**
 - 0 = Black
 - 1 = Brown
 - 2 = Red
 - 3 = Orange
 - 4 = Yellow
 - 5 = Green
 - 6 = Blue
 - 7 = Violet
 - 8 = Gray
 - 9 = White

- Differentiating stalactites from stalagmites:

 **The 'mites go up and the 'tites come down**

- 10 organ systems of the human body (Nervous, Integumentary, Circulatory, Endocrine, Respiratory, Digestive, Reproductive, Urinary, Muscular, Skeletal):

 **NICER DRUMS**

## Geography

- The Great Lakes in order of largest to smallest (Superior, Huron, Michigan, Erie, Ontario):

 **Super Heroes Must Eat Oats** (or **SHMEO**)

- Major cities of Australia (clockwise): **BSC MAPD H**:

 Brisbane, Sydney, Canberra, Melbourne, Adelaide, Perth, Darwin, Hobart

## Chess

- Setting up a chess board (Bottom right corner for both players must be a light square):

 **White on the right**

- Philidor vs Lucena:

 **Philidor** position is a **drawing** technique. Both words have a "d" (for draw). 
 **Lucena** is a **winning** position. Neither word has a "d".

## Number of days in each month

It's easy to remember that February has **28** days in a common year, and **29** days in a leap year, which occurs every four years (except for century years not divisible by 400).

To remember that **April, June, September, and November** have **30** days, use any of the following mnemonics. All the rest have **31** days.

- The one I use, which I came up with in middle school: **SNAp June**
- The one that I taught my 5yo nephew: **ape-jun-se-no**
- Numeric: **4 6 9/11**
- In Roman numerals: **IV/VI IX/XI** (each contains exactly two unique letters and each pair is a mirror of the other)
- [Knuckle mnemonic](https://en.wikipedia.org/wiki/Knuckle_mnemonic)
- [Thirty Days Hath September](https://en.wikipedia.org/wiki/Thirty_Days_Hath_September)

 ```plaintext
 Thirty days has September,
 April, June, and November,
 All the rest have thirty-one,
 Save February at twenty-eight,
 But leap year, coming once in four,
 February then has one day more.
 ```

## Misc

- Confronting a screw:
 
 **Righty-tighty, Lefty-loosy** or **Right on, Left off**

- Identifying coral snakes:
 
 **Red touches yellow, kills a fellow. Red touches black, friend of Jack.**

- The first 11 (and most important) Ionian philosophers (Thales, Heraclitus, Empedocles, Leucippus, Anaximander, Democritus, Zeno, Anaximenes, Protagoras, Parmenides, Anaxagoras):

 **THE LAD ZAPPA**

- Daylight savings time:

 **spring forward, fall back**

## Links

- [List of mnemonics](https://en.wikipedia.org/wiki/List_of_mnemonics)