# RIDDÅL - another unfinished flat-pack puzzle

This is an entry to the 19th Fortnightly topic challenge

Yesterday I got a package in the mail. Attached to its top was a letter:

Dear Alconja,

That's strange, I thought... Must have gone to the wrong user.

As a result of your excellent choice in purchasing a REJBÄS puzzle, you have been invited to user test the new RIDDÅL puzzle. It is intended to be harder and more complicated than the REJBÄS and to have more ambiguous instructions.

Thank you!

N.B. Also, once you open the package the materials will self-destruct in exactly one minute.

So I got my scanner ready and opened the package. There was an instruction booklet, a trapezoidal grid tiled by triangles with letters and a black and white hexagon, also tiled by triangles and with an arrow and the code PLZ-SE-95R.

I couldn't make heads or tails of it, so I wondered whether anyone could solve it for me. Maybe Alconja themself could solve it...

Anyway, here are the scans. They got progressively worse as the minute ticked down:

The instruction booklet

The trapezium

The hexagon

Notes:

• They weren't scanned to the correct size.

• The trapezium was printed on both sides, but was printed as if the ink had gone straight through the cardboard (so I didn't scan it).

• The hexagon was printed only on one side

• The link to the instruction booklet has a PDF on Dropbox

• The number in step 13 is, to the best of my knowledge, 67857383296491225625081879653534944430162017097746438655845348065271398002936105813847401195885432.87149223286951755978260113706096896662684272363707639031761219104950570374243315214582045841

Credits:

Alconja for the inspiration (here) and some of the images.

This book series (will be was revealed when the puzzle is was solved) for the riddle...

Hints:

1. (Step 1)

The first step isn't totally necessary from a puzzle-solving point of view, but is needed for where one of the stipulations is

2. (Step 1)

The crosses in the first step symbolise something other than 'don't cut'

3. (Step 1)

Step 1 is purposely ambiguous - it is not meant to be taken literally

4. (Step 2)

The shapes in step 2 are meant to be generic

5. (Step 2)

The r's in step 2 could plausibly represent two things - they represent both...

6. (Step 2)

This step is easier to do mechanically than on a computer

7. (Step 3)

The black triangle isn't just any triangle

8. (Step 3)

You need to make an observation about a seemingly innocuous aspect of the puzzle to do this step

9. (Step 3)

This step requires the previous step unlike step 2

10. (Step 4)

Is there something asymmetric about the picture?

11. (Step 4)

This should only be done once

12. (Step 4)

It should be applied to an object, not the absence of one

• By the way, since there are many steps involved in solving the puzzle, a progress post might be helpful. Commented Nov 2, 2016 at 2:25
• Do we not have any pieces like the last one? Commented Nov 2, 2016 at 7:08
• Step 4 is likely to be "leapfrog", since it's a frog with the leap day date on its back. Commented Nov 2, 2016 at 15:25
• I'm pretty sure they are instructions for an ikea furniture Commented Nov 19, 2016 at 3:30
• ...you keep adding hints further and further into the puzzle, but has anyone actually worked out how to deal with step 2 yet? Not much point providing hints to step 4 if we can't even get there... Commented Dec 18, 2016 at 10:16

## Step 1

This is a small section of the trapezoid, so we need to cut the trapezoid apart (maybe into each triangle, maybe into different pieces)

And don't cut apart the hexagon with PLZ-SE-95R (?)

## Step 2

Transform the trapezium into the hexagon by following the path of an S (snaking) for the input and spiraling inwards for the output. You'll notice that doing this on the trapezium would seem a bit off as you end up with non-alternating directions.

This can be fixed by following the accompanying text of r0r180r0r180r0. This corresponds to the five rows on the trapezium. Rotate the second and fourth rows.
Here are the diagrams for the transformation:

## Step 3

After the transformation we notice that one spot is missing. The black triangle on the instructions refers to that, so draw a line straight down from it.

## Step 4

Leapfrog (from Dan Russell)

Hop over to the right, twice.

## Step 5

We can fill in the blanks with WD, forming WD-40, a well-known lubricant.

Draw a line from the single W to the single D.

## Step 6

Swap the two sets of two triangles along the pivot.

## Step 7

As in Step 4, we will be flipping triangles into the hole. The side and order is specified by the - \ / sequence.

## Step 8

Draw lines! On the entire 96 triangle hexagon formed from step 2 and whatever other transformations may have occurred.

## Step 9

Flip horizontally the triangles inside of the areas specified.

## Step 10

There is only one section of the puzzle where you see that pattern of marks we've made (on the right side). Apply the transformations to that set of triangles.

Draw a line.

## Step 12

Completely fill triangles that look like that (with the line through it)

## Step 13

Can be broken up into 96 pairs (. being a pair, maybe confirming that we have an empty space). A reordering of the triangles.

Sequence: 67 85 73 83 29 64 91 22 56 25 08 18 79 65 35 34 94 44 30 16 20 17 09 77 46 43 86 55 84 53 48 06 52 71 39 80 02 93 61 05 81 38 47 40 11 95 88 54 32 .  87 14 92 23 28 69 51 75 59 78 26 01 13 70 60 96 89 66 62 68 42 72 36 37 07 63 90 31 76 12 19 10 49 50 57 03 74 24 33 15 21 45 82 04 58 41Index:    01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

## Finally

I must've done something funky, but taking the letters from left to right, top to bottom, we have

GURNFAJREGBGUVFEVQQYRUNFNUBYRAGURZVQQYVNAQFBZRUNIROAXABJAGBSNYYVVGVAGRAAVFVGFABGUVATOHGGPNAORERPRVIRQNAQFBZRGVZRFNCREFBAZNLJVAVGGUBHTAUBGFRRABEURNEQVGZLLRGORCREPRVIRQYVXRCEVAPRFBEORRFVGFVAPYBIREGURNAFJREGBGUVFEVQQYRUNFNUBYRVAGURZVQQYRNAQJVGUBHCNVGBAOPNAABGCGNEGSIREKK

The resulting image clues us to ROT13. We get:
THEASNWERTOTHISRIDDLEHASAHOLENTHEMIDDLIANDSOMEHAVEBNKNOWNTOFALLIITINTENNISITSNOTHINGBUTTCANBERECEIVEDANDSOMETIMESAPERSONMAYWINITTHOUGNHOTSEENORHEARDITMYYETBEPERCEIVEDLIKEPRINCESORBEESITSINCLOVERTHEANSWERTOTHISRIDDLEHASAHOLEINTHEMIDDLEANDWITHOUPAITONBCANNOTPTARTFVERXX

THE ASNWER TO THIS RIDDLE HAS A HOLE N THE MIDDLI AND SOME HAVE BN KNOWN TO FALL IITIN TENNIS ITS NOTHING BUTT CAN BE RECEIVED AND SOMETIMES A PERSON MAY WIN IT THOUGN HOT SEEN OR HEARD IT MY YET BE PERCEIVED LIKE PRINCES OR BEES ITS IN CLOVER THE ANSWER TO THIS RIDDLE HAS A HOLE IN THE MIDDLE AND WITHOUP A IT ON B CANNOT PTART FVERXX

It seems that the answer to this riddle is: LOVE

The hole is the letter 'O'.
In tennis, love is a term for the score 0, which is nothing.
...something about winning it and being perceived like princes and bees...
CLOVER
And I can't make sense of the end.

• Indeed it is easier to do it manually, it was a pain for me to digitalise it all. If you post progress at each step (take a picture if you're doing it by hand), I'll tell you whether you're on the right track or not. What's stopping you from continuing? Commented Nov 29, 2016 at 4:34
• @boboquack I've been busy, I stop by whenever I can, but don't have too much time. Commented Dec 2, 2016 at 1:20
• It's been more than a week...
– Deusovi
Commented Dec 2, 2017 at 0:28
• One week later.... Commented May 29, 2018 at 8:13
• Wow, great work! Unfortunately I have lost my notes for this puzzle in one spring cleaning or another, so I can't say which step didn't work out completely well, but I can confirm the final answer is correct! Looks like whatever bounty I said I was going to award went astray, here's another one for good measure. Commented May 29, 2018 at 8:16

When rotated and mirrored (note says ink went through) to align the letters there are 47 triangles that point upwards and 46 that point downwards with 2 triangles that could work either way. There are 95 faces overall, which is 5×19.

There are 1 M, 1 D and 1 W in the trapezium, all the other letters have several occurrences.

Transcription of the trapezium:

Triangles that point upwards, letters are top, mid, left, right:
UNCV, VRRO, TJSW, QPCK, SIKX, IFGG, EENF, AAVA or AAAV, AGBG, RFBI, SXAZ, ICOS, BQNI, LTLS, COLK, SHJT, FRUV, VRAV, BFBG, YFHG, NRBE, JKLZ, VNFE, GRUV, JGQY, RRRU, HTST, BQJV, UECE, JSCO, CCTO, FVZR, TXZK, LHTS, RVLJ, AGGP, FGGB, UAAX or UAXA, NGEV, RRQF, FEAU, YFQQ, ANEK, ORAZ, VVPR, ZBFR, NCBH

Triangles that point downwards, letters are left, right, mid, bottom:
AGRH, FABQ, VYUB, COCI, HIQP, PRZV, VAAA, UNZB, YRQG, RACX, ZIMH, GZIF, GBAT, QPQK, RNPV, AGNR, VGUG, BERR, NUVQ, AQRT, NUQU, DCOV, JXST, YRYR, ORVR, BJRU, PNGR, RQNU, OZHL, ZCLK, UREF, HOOI or OHOI, HTIJ, LLQO, SNVO, EQRA, RGYR, BAGG, YVVV or VYVV, ABEK, RZAG, BIJY, XZZK, AAPV, VGFN, REGN

Triangles that could point either way:
If downwards: HHIH, IKKK
If upwards: HIHH, KKKI

Letter occurances:

AAAAAAAAAAAAAAAAAAAAAAAAAAA
BBBBBBBBBBBBBBBBBBB
CCCCCCCCCCCCCC
D
EEEEEEEEEEEEEE
FFFFFFFFFFFFFFFFF
GGGGGGGGGGGGGGGGGGGGGGGGGGG
HHHHHHHHHHHHHH
IIIIIIIIIIIIII
JJJJJJJJJJJ
KKKKKKKKKKKKK
LLLLLLLLLL
M
NNNNNNNNNNNNNNNNNN
OOOOOOOOOOOOOO
PPPPPPPPP
QQQQQQQQQQQQQQQQQQ
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
SSSSSSSSSSS
TTTTTTTTTTTT
UUUUUUUUUUUUUUUU
VVVVVVVVVVVVVVVVVVVVVVVVVVVV
W
XXXXXXX
YYYYYYYYYY
ZZZZZZZZZZZZZZZ


Another observation:

Based on the letter frequency compared to English a shift by 13 characters makes sense.

• Good start! Now start doing each step in turn. Commented Nov 2, 2016 at 20:07
• However, you haven't got the correct number of triangles on the trapezium. Commented Nov 2, 2016 at 20:10
• Hint: The top-right triangle is oriented the right way up: it is ZIMH Commented Nov 3, 2016 at 0:07
• @boboquack Welp, I assumed default fonts where the M and W are different and this looked like a W. Also this post was mainly meant as a help for others. But when I have more time, I will definitely try to solve it.
– w l
Commented Nov 3, 2016 at 8:16
• Unfortunately Futura (IKEA's font) doesn't distinguish very well. Commented Nov 3, 2016 at 8:39