# A Page of Puzzling

I found this puzzle page from a newspaper and found it absolutely confounding. The sudoku had question marks and other things all over it, the logic puzzle made no sense, the cryptic crossword was missing any markings (and the clues weren't numbered, or in order!).

I thought I got my puzzling's worth out of the anagram, alphametic, and maze, until I realised there was something more fiendish going on here. I eventually managed to find a three word congratulatory message that was well hidden inside all these puzzles!

Can you solve all the puzzles and find the message?

NOTE: I've made a tiny tiny edit to the page. There were no mistakes in the previous page, the edit is practically superficial, but it might make the going a bit easier if you notice it.

• Observations: page number is suspicious, "dashed line" on sudoku too so they should correspond somehow, mega maze probably traces path on sudoku, this looks like a really well made puzzle. Dec 21 '16 at 19:42
• Re: Numbers. How can they have 8 unique digits? Given that 1000 is the maximum, can't there only be 6 unique digits assuming 2 different 3 digit numbers? EDIT: Ignore me, there are 3 people in that conversation :P Dec 22 '16 at 3:21

The solution is

"Well done, love"

The crossword was first solved by @NeilW, and @Sconibulus solved the alphametic and the maze (go upvote them!).

For the Sudoku:

There are 8 question marks, which seem to correspond with the question marks in the crossword clues. Assigning each question mark the appropriate value, we get 5 1 7 6 2 3 1 4 (9) along the main diagonal.
The dotted line with the circle at the end is the same as the one in the logic puzzle, so the solution to the Sudoku will help fill in the logic puzzle.

For the Anagram:

The recent edit circled the page number, connecting it to the circles in the anagram puzzle. Due to @Arth, it can be translated to REMOVE ALL using the alphametic. We can then remove ALL from the letters, leaving us with E R W A F T.

For the Logic puzzle:

(After a nudge from the OP) The ostensible misspelling of "Margana" is actually an anagram of, well, "anagram", linking the logic puzzle to the anagram. Note also the ellipsis when Margana is about to say her type of number, and the ellipsis at the end of the anagram puzzle. We can't anagram the letters directly, but noting the strange discrepancy in font, we can actually rotate the W to become an M, giving us FERMAT.
Using this, we can deduce that the numbers have to be:
- Mersenne: 31
- Perfect: 496
- Fermat: 257

Back to the Sudoku:

The "correct" solution to the Sudoku, then, would use those numbers along the dotted line. If we try to solve the Sudoku with the numbers given, we get a 7 in the box in row 5 and column 6. This allows us to fill in the numbers on the dotted line by deduction, ordered 31, 257, and 496.
From here, we can solve the grid (thanks @LeppyR64 for solving a critical step in the sudoku!):

Finally to the Maze:

The maze looks just like the Sudoku grid, suggesting that we can overlay it onto the Sudoku (as @Sconibulus suggests). Note that "jump from an arrow" is underlined, hinting that the code from the alphametic should be applied to the squares where we made a jump. The numbers in these squares, in order, are: 6, 7, 8, 8, 2, 4, 1, 7, 8, 4, 3, 7. If we then apply the alphametic code, we get WELLDONELOVE, which clearly leads to the solution.

• Congratulations! First to find the final message :) I might wait a bit until either the sudoku gets solved and/or a comprehensive solution covering the whole process gets put up. Dec 22 '16 at 8:15
• For the Sudoku. (Letters are rows, A1 on top left) C1 has {3,6}, G1 has {6,9}, G5 has {3,9}, C5 has {1, 3}. If C5 were 3 then C1 would be 6, forcing G1 to 9, leaving G5 without a possibility. C5 must be 1, forcing the rest of the solution. Dec 22 '16 at 13:11

MAZE

If we overlap the maze results on the SUDOKU we get 659 497 5419 251 4782 695 63 47 832 81 42 827 5 that was an older version of the maze, and the wrong Sudoku result

ALPHAMETIC

A=9 N=1 M = 0 R = 5 O = 4 W=6 E = 7 D = 2 V = 3 L=8
ARMED-WAR=AOVEE
95072-695==94377
ARM + ARE = NAME
950+957==1907
ELM-DEW = RMO
780-276==504

NUMBERS

There has to be some trick to this I'm not seeing, because it looks impossible.
Mersenne Primes < 1000 = 3,7,31,127 @Leppy points out that this can be narrowed to 31 or 127 for Merlin's Number
However, Mersenne Numbers are different than Mersenne Primes (thanks @Arth for pointing this out) so that extends to {31, 127, 255, 511} Perfect Numbers < 1000 = 6,28,496 @Leppy points out that we can narrow to 496 being Mildred's number.
Numbers < 1000 (there's about a thousand)
I don't see how this can resolve to a unique solution.

ANAGRAM

WATERFALL

CRYPTIC CROSSWORD

@Neil W came up with this first, but I verified it and added (most of) the explanations (incidentally, the italics lined up with roman numerals, which explains ROMAN in italics in the header. D
MIX (SCRAMBLE OVER A THOUSAND)
SLOW (Leisurely, confused night birds)
IDOL (Similarly lazy (idle) figure)
A
NEW (Sounds like you, Are Original)
XENO (Lonely (one) Crucifix (x) Returns Stranger)
EDEN (ABNORMAL REQUIREMENT(NEED) for a Fruitful Garden)
?ONE (Perform(ed) any sound)
TOTAL:

MEDS
IDOL
XENO
NEW
In what may be a staggering coincidence, the three letters (and blank) not convrtable with the Alphametic are S,I,X. If we call that 6, and then take 0,1,2,4,6,7,8 (the numbers the others conver to) we have eight distinct digits! Unfortunately none of them are 9, so this doesn't really help with the Number game.

PAGE NUMBER

Apply the ALPHAMETIC to it, and we get REMOVE ALL (Thanks @Arth)

• Can't "E" in the 2nd one be 3?
– Sid
Dec 21 '16 at 16:12
• @SID I couldn't make any of them unique alone, so I assumed that all three equations had to be solved simultaneously Dec 21 '16 at 16:13
• Haven't you crossed a solid line to get to the red square? Dec 21 '16 at 16:29
• @NeilW Oops, didn't see that, fixed in a moment Dec 21 '16 at 16:32
• Lol, left that one in the list. Sorry about that. Was supposed to be 3, 7, 6, 28. Dec 21 '16 at 17:08

Cryptic Crossword

Letters / Clue numbers

 M E D S  /  1 2 3 4
I D O L  /  5 - - -
X E N O  /  6 - - -
- N E W  /  - 7 - -  
Across clues: 5, 1, 7, 6. Down clues: 2, 3, 1, 4.

Similarly (homophone) lazy (idle) = IDOL = figure
I (me) start with five hundreds (D's, roman numerals) = ME+DS = pills
It sounds like (rhymes with) you = NEW = original
Lonely (one) crucifix (cross=x) returns = X+ENO = stranger (greek prefix)
Abormal requirement (need) = EDEN = fruitful garden (biblical garden with forbidden fruit)
Perform (do) any sound (n,e) = DO+N,E = performed
Scramble = MIX = over a thousand (1009, in roman numerals)
Leisurely = SLOW = confused night birds (owls)

# Wrap-up: The Making Of A Page of Puzzling

This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.

Caution: This post may contain spoilers.

### Inspiration

I've had the idea for a while to do a newspaper-esque page of puzzles that actually link together, but it always seemed like a fairly daunting task to make a large set of 'common' type puzzles that had to be solved in conjunction, so I put off the design until I had the idea of a sudoku with sets of numbers that could be deduced from other puzzles.

### Creative steps

No newspaper puzzle page is complete without a sudoku, so once I had the idea of having some numbers that had to be taken from other puzzles, I decided to design the rest of the puzzles around the sudoku.
Most newspaper puzzle pages have cryptic crosswords, too - but before this puzzle, I had absolutely ZERO experience with writing cryptic clues, so I was a little hesitant to include anything cryptic. Eventually, I decided to make a very mini crossword, but knowing the cryptic abilities of PSE, I had to make the mini cryptic harder somehow - why not put the clues out of order? And maybe the order of those clues could be some numbers for the sudoku... hmm...

I then had the idea of a 9x9 maze that would somehow link with the sudoku, most likely to spell out the final message. But how to turn the digits 1-9 into letters without putting obvious encryptions anywhere on the page? An alphametic, of course. Once I decided to include a maze and an alphametic, both 'miscellaneous' puzzles, I decided to include a 'Brain Trainers' section that would need another puzzle or two to bulk up. At this point, I decided this was probably enough!

### Logistical steps

I started with writing the cryptic clues, given that I had the least experience with these. I started off by making the crossword, and then created clues to fit the words I had put into the 4x4 shape. I've apparently broken some sacred cryptic rules (indirect anagrams...), but I think my clues were easy enough that these sins seem to be mostly forgiven :)

I picked a random order for the clues, and decided they would go along a diagonal of the sudoku - the sudoku was probably the hardest section to design. I wanted to signpost somehow that the sudoku was NOT the place to start - so I made the given clues very, well, arbitrary. A cell with '123456789' and then hints that went '876' and '765687'. I decided I would need more outsourced for the sudoku, and thought that the easiest way to get numbers from another puzzle, is to have a puzzle where you need to deduce numbers!

The logic puzzle was me trying to condense finding very specific numbers into a small space. Mersenne, Perfect, and Fermat numbers are fairly rare, which meant that the puzzle would become expressible within a few lines. Being a little bit evil, like I am, I wanted to mess up the puzzles a little more by making the logic puzzle incomplete... so I left out 'FERMAT', thinking that I could clue to it in an anagram puzzle with the M upside down as a W!

At this point I realised I was kind of going all out with the messed up common puzzles. So, why not mess up the anagram puzzle as well? I knew FERWAT did have an actual solution of 'WAFTER', but I thought adding in some extra letters that should later be removed would be fun (why not?), so I extended it to 'WATERFALL'. What letters are extra? 'ALL'. That's kind of nice. So I need to hide 'REMOVE ALL' somewhere in the page. Hmm.

Having not decided what the final message would be, yet, I decided to put these letters, R E M O V A L, into the alphametic. Aghhhh! Now I need to make sure the alphametic clues at both 'REMOVE ALL', and makes some sense with the sudoku and the maze.

Since the sudoku finally defined, now that I added in the special numbers along another diagonal, I thought, 'It's going to be way too hard to hide a nice message in a sudoku that I kind of arbitrarily defined'. So the maze had to be done in a way such that I could specifically choose numbers from the sudoku at will - and the hypermaze idea came not too long after that. A quick thought about available letters led to the message 'WELL DONE'. Deciding this would make the maze route too short, I extended it to 'WELL DONE LOVE'!

At this point the rest of it was sorting out details. Making the maze and making the alphametic were fairly tedious jobs that just needed to be done, and adding in the page number, the puzzle was essentially complete.

### Signposting

Signposting is a term I use to describe 'unusual or unnecessary details that, once noticed, will put the solver on the right path'. Given that there were quite a lot of steps in this puzzle, I decided that I should put in a LOT of signposts.

Some signposts were just necessary for the puzzle to work - for example, the question marks in the sudoku+crossword, and the dashed line in the sudoku+logicpuzzle, as these were links that had to be very specific.

I put in the italics link because initially the clues involved the word 'ROMAN', which was a bit clunky, but Roman numerals I thought were a bit of an unfair leap in solving without any clues.

There are a lot of numbers and letters - so I needed to clearly show where and how the alphametic would be used. Bold is too obvious, and was already being used in the cryptic. So, underlining was the easy option.

I had to signpost the rotation of the W in the anagram, and I thought the easiest way to do this was to construct a situation where the letters could be rotated without much effort. Hence the 'plates' story, as well as the dreaded comic sans font :P

I thought the link between the anagram and the logic puzzle had to be fairly clearly done, otherwise it could be a bit of a dodgy step. So, I signposted it twice! Once with ellipses, and once with an anagram/mispelling.

Signposting is actually one of the more fun parts of puzzle design (for me) so it was a great way to finish off making the puzzle. I hope you all enjoyed this page of puzzling as much as I enjoyed making it!

I am here just for the alphametics part

ARMED - WAR = AOVEE (1)
ARM + ARE = NAME (2)
ELM - DEW = RMO. (3)

subtracting E from both sides we get ARM + AR0 = NAM0. We immediately see that M = 0 so now we have AR0 + AR0 = NA00. Dividing by 10 we get AR + AR = NA0. So R can be 5 or 0, but M is already 0 so R= 5. And the only value for A that fits is 9 to get 95+95 = 190.

Recap with what we have.

950ED - W95 = 9OVEE (1)
950 + 95E = 190E (2)
EL0 - DEW = 50O. (3)

Using (1)...

subtracting 90000 from each side we get 50ED = OVEE + W95. This means O is either 4 or 5, but 5 is taken. SO O = 4.

Recapping

950ED - W95 = 94VEE (1)
950 + 95E = 190E (2)
EL0 - DEW = 504. (3)

Using (3)

we can clearly see that W = 6 because we need to get 4 by subtracting W from 10.

Recapping again.

950ED - 695 = 94VEE (1)
950 + 95E = 190E (2)
EL0 - DE6 = 504. (3)

Using (1) again...

and subtracting 94000 and $E*10$ from each side we get.
100D - 695 = V0E
This means that V can be 3 or 4, but 4 is already taken, so V = 3.

The usual recap:

950ED - 695 = 943EE (1)
950 + 95E = 190E (2)
EL0 - DE6 = 504. (3)

Now we only have the available numbers and letters.

2, 7 and 8 for E, L and D.

From (3) we see that..

E is way bigger than D (at least a difference of 5). This means that D = 2.
Rewriting 1 with what we found: 950E2 - 695 = 943EE. This immediately gets us E = 7 (because E = 12 - 5).
Now we only have one letter available and one digit. L = 8.

Let's see if they all fit:

95072 - 695 = 94377 (1)
950 + 957 = 1907 (2)
780 - 276 = 504. (3)

Yep, they fit.
Conclusion:

M=0 N=1 D=2 V=3 O=4 R=5 W=6 E=7 L=8 A=9

Partial findings - >

ANAGRAM

WATERFALL

Number's

If there are no specific rules on how many digits each of the three have to write, the numbers were Merlin 12_(127), Mildred-4_6(496), Margana 0583(0583 - Not sure if 0 is allowed as prefix. This is considering that she wrote the numbers between others.) So, the unique numbers on the dashed list were 1,2,4,6,0,5,8,3

SUDOKU

The sudoku grid looks like ->

CRYPTIC CROSSWORD

Perform(ed) any sound(4) - > ABLE -> Perform(ABLE) , Able -> Sound
Lonely crucifix returns stranger(4) - > ROOD-> Crucifix(ROOD) -> DOOR(Returns stranger) Scramble over a thousand(3) -> MIX -> MIX in Roman = 1009(Thanks @Sconibulus)
It sounds like you are an original(3) - > ONE

• I'm not sure about protocol here. When the OP asks "Can you solve all the puzzles and find the message?" aren't we supposed to wait until we've accomplished that task before posting an answer? That's kind of the point, isn't it?? Dec 21 '16 at 15:56
• @wildBillMunson- We are allowed to post the findings(partial answers). Spoiler tags help you not to look Dec 21 '16 at 15:59
• OK good to know. Dec 21 '16 at 16:01
• Your Mildred's number isn't perfect Dec 21 '16 at 16:21
• @Sconibulus- Yeah. Names were interchanged. Edited. Dec 21 '16 at 16:23

Sudoku:

Alphametic:

ARM + ARE = NAME 950+953==1903

Sudoku (solved BY HANDS):

which gives diagonally (on the question marks) : 2 6 7 6 1 2 3 7 9

• Is this a unique solution? Because it feels like the ? line should line up with the ?s in the cryptic (i.e., correspond to the order of the clues), and the dashed line should match the dashed line in the logic puzzle (i.e., be 8 unique numbers). Dec 21 '16 at 16:48
• According to a solver I used it is unique.. I also found this frustrating!
– Arth
Dec 21 '16 at 18:58
• I even went so far as to overlay the dotted lines onto the map and transpose each number according to the arrows.. but it didn't help :(
– Arth
Dec 21 '16 at 19:02

I think the 2 most useful clues we have are:
1) a three word congratulatory message that was well hidden inside all these puzzles!
2) And the easiest to solve puzzle, being the Anagram.

Then if it's the same three word message found in every puzzle, then we only need to find it inside one puzzle.

"waterfall" has 9 letters. therefore it's like that the 3 word puzzle made of 9 letters is 3 3 letter words. All the 3 letter words that can be made are:
aal aft ala ale all alt are arf
art ate awa awe awl ear eat eft
elf ell era eta far fat fer fet
few lar lat law lea let rat raw
ref ret tae tar taw tea tel tew
twa wae war wat wet
thanks to word finder, there may be other combinations than 3 by 3.

If it's a combinatory puzzle, where each puzzle has a word, then it may be more difficult.

Edit: There are 6, possibly 7 (Page 57043798) puzzles there and the wording is a bit ambiguous: "a three word congratulatory message that was well hidden inside all these puzzles"
Have to think either: How can 6 puzzles create 3 words? -or- How can 3 words be hidden in 6 puzzles?