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### Solutions for Act V Scene 4 - Cards

This puzzle provides us with five colour-coded decks of cards. The first obvious thing to note is that all the cards on the left half spell out words, most of them proper nouns. A bit of research will reveal most of these are people and characters famous for doing or a being a particular thing - for instance NERO was a Roman Emperor, while HADES was the Greek god of the underworld. We also have some common words like RESTRAINT and MIGHT, while other words don't seem to fit into any particular category, like ENDOR. The key here is to realise that the 22 lines correspond to the 22 Major Arcana Tarot cards in some order. The order can soon be worked out to be as follows:

 Clue Card Crennan Justice (11) restraint Temperance (14) Nero The Emperor (4) Eunapius The Hierophant (5) Sol The Sun (19) Hades The Devil (15) Vega The Star (17) Grim Death (13) might Strength (8) Feste The Fool (0 or 22) earth The World (21) gameshow Wheel of Fortune (1) Eiffel The Tower (16) Harrill The Hermit (9) Endor The Moon (18) Tom Horn The Hanged Man (12) Jito The Empress (3) Romeos The Lovers (6) Potter The Magician (1) Nimueh The High Priestess (2) decree Judgement (20) wagon The Chariot (7)

As given above, each Tarot card is associated with a number from 1-21, with The Fool having number 0 or 22. This is promising, since on the right half of the puzzle we have a series of equations waiting to be filled in. Clearly the cards given need to be placed in some order, and in all likelihood we want each equation to equal the number associated with its corresponding Tarot card. It also seems clear the number each card stands for should be its normal card value, where Ace = 1, Jack = 11, Queen = 12, and King = 13 (some of these values might be ambiguous, but can be confirmed after trying a few examples). For example, the first line should equal 11 to match with Justice, so we find the suitable arrangement 10/2-3+1*9. Of course, the 9 and 1 could be switched here. The equations required turn out to be:

• 10/2-3+1*9
• (3-8)*2+12+12
• (2/2-10)/3+7
• (7-9)*3+11
• (12-7-1)*8-13
• (12/4+9-9)*5
• 6*4/2-1+6
• (6-6)*3+13
• (6+5-7)*8/4
• (12+5)*13-1)/10 (for 22)
• ((8-11)*3+12)*7
• 5/5+8+1
• (11+4)/5*4+4
• (7+10)*11/11-8
• (13/13)*10*3-12
• (6*13+6)/7
• (1+13-8)/3+1
• (2-10)/8+9-2
• (13-9)*11/4-10
• (11+11)/2-9
• (9-12+7)*5/1
• 6*5/10+4

Note there are a few areas where order is not completely determined. Wherever applicable, a green card should have gone before a purple card of the same value, as hinted at by the way the piled cards are given (and conventional rainbow order). But the easiest way to determine we have the right ordering per row is to realise we need to use the letters on these cards somehow. Reading down each column in turn, fixing ordering where necessary, we can see the message COLLECT THE PRIMARY CARDS WITH FIRST CARD ON TOP, THEN PUT EACH CARD INTO HIGHEST ROW IT CAN LIE IN - E.G. SECOND R GOES INTO THIRD ROW. Hopefully this message is not too ambiguous - it seems we want to reorganise the primary-coloured cards in some way, and the first step should be to pick them all up in order, with the first card being the top of the pile and the last card the bottom.

Now the question remains how to reposition these cards. Keeping in mind there are also a lot of spare letters given by the leftover cards at the bottom, the intuitive leap here is to realise there are exactly enough letters to spell out each of the Tarot card's names, if we ignore the "The"s. Assuming this, the first card, a C, will be placed in the top row, since we know its corresponding card is JUSTICE, which contains a C. The second card is our first R, and it will be placed in the second row since there is no R in JUSTICE, but there is one in TEMPERANCE. When we come to the second R as per the example in the message, it will indeed be placed in the third row, since JUSTICE contains no R, the R in TEMPERANCE has already been filled, and EMPEROR requires an R.

Redistributing in this way gives us an entire board of placed cards. Now we just need to work out what to do with this new ordering. Another hint is hidden in the cards on the left, which was unfortunately not able to be hinted at in itself, but hopefully most people were on the lookout for this sort of hint anyway. If we look at the spades of each primary-coloured deck in order, a message can be read by reading off the red spades Ace through King, then yellow spades Ace through King, then blue spades Ace through King (the suit of spades was chosen because the Ace of spades is large and attention-drawing). This messages reads FIRST LETTER'S J, SO ADD THE FIRST TEN CARD VALUES.

Most solvers should immediately recognise why the letter J and the number 10 are being linked here - because J is the tenth letter of the alphabet. Clearly our first card is indeed a J from JUSTICE (if this message was discovered earlier, it hints at the previous step). What constitutes the "first ten" cards in this case is slightly ambiguous - we could take the first ten on the left-hand side, or the first ten overall, running over the dividing line. This latter interpretation turns out to be the one we want, and hopefully makes sense given we have yet to use the ordering of the card values we found on the right-hand side.

The other question is what the second letter is, and how many cards we should read off from that. Again there are a few interpretations (second letter of JUSTICE, the eleventh card on the board, etc.) but hopefully the most natural assumption is to use the first letter of the second Tarot card, i.e. T from TEMPERANCE. If we do assume this, we can note the sum of the first letters of each card (J+T+E+H+S+...=10+20+5+8+19+...) is in fact 260, exactly the number of cards in the puzzle. This confirms this step, and so if we add the first ten card values, then the next twenty, etc., we get a series of large numbers: 66, 135, 24, 46, ...

How can we turn this into a message? The tempting thing to do here is check the numbers' residues mod 26 (13 could also be a possibility based on the cards theme, but it would be unlikely to have a message made up of letters only from A-M). This is promising, since the first few numbers become 14, 5, 24, 20, ... which corresponds to the letters NEXT. All up we get the message NEXT TRY BY SECOND LETTERS.

Following this suggestion, we notice that remarkably, the sum of all the second letters of the Tarot cards (U+E+M+I+U+...) also equals 260. So we can perform the same trick, and this time the message we extract is TAROT STATUE PARK CREATOR. This is a reference to the Giardino dei Tarocchi, or The Garden of Tarot, a sculpture park crafted by the French artist Niki de Saint Phalle.

Design Notes: This puzzle was really just a showcase for the amazing coincidences contained in the English names for the Tarot Major Arcana (excluding the "The"s, of course). I had wanted to do a semi-research puzzle about the Major Arcana for a while because they have such a range of meaning in their names, and one day decided to count up the number of letters they total - I hadn't bothered writing out each "The" out of laziness. When I realised the total was a multiple of 52 I knew this had the makings of a puzzle. When I considered adding up the first letters' values and discovered this too was a multiple of 52, I knew this had to be a puzzle! After that I wrote a quick program to check for other multiples of 52, and couldn't believe my luck when it turned out the sum of the second letters of each card in fact equalled the sum of the first letters. I hope people enjoyed discovering these coincidences as much as I did!

Some of the synonyms were fairly tentative - e.g. Nimueh is apparently referred to as a High Priestess in the series Merlin often enough, but Wikipedia doesn't use the full term. My goal was to go for words that were fun in some way, so as often as possible I tried to avoid the obvious name to attach to each card. I was extremely tempted to clue Temperance with "Bones" or similar but unfortunately there were no B's to play with. I also had come up with a set of words that only left 22 spare cards (including "Romeo and Juliet" for Lovers), but managed to lose that list and had to make do with my second-best. This was probably for the best since having exactly 22 spare cards might have been a tempting red herring.

The original draft for this puzzle had some of the cards face down, because I wanted to emphasise the fact five full decks of cards were being used, and figured having to work out the missing cards would contribute to this. The left and right decks mingled more in this version too, since instead of letters, the green and purple decks had mathematical symbols on them and were used as the printed ones are in the final copy. Unfortunately this set-up just proved too unwieldy and impossible to construct without sacrificing the last, second-letters step, which I definitely wanted to keep.