5D Barred Diagramless with Multiverse Time Travel

This puzzle is both a barred diagramless crossword and a reference to 5D Chess with Multiverse Time Travel. We should first solve the crossword, then solve the 5D Chess problem.

The crossword

As suggested by the given diagram, there are three 13 × 13 barred diagramless grids to fill in. This is supported by having three 1 downs, three 2 downs, and so on.

There are a few gimmicks to the crossword fill.

• First, there are occasional 1-length entries that do not have crossword clues. This will likely be discovered by trying to assemble the diagramless, but can be guessed based on the given numbers. In a standard diagramless, there should be 13 down clues starting from the top row, giving three 1 down, 2 down, 3 down, etc. up to three 13 downs. We do not have three 13 downs in the given clues, which is only possible if we skipped one of the potential down clues.

• Second, there are a few strangely worded down clues, like "To burn tea" or "Japanese comic about skin disease". These clues have two answers that differ in one place, like CHAR / CHAI and MANGA / MANGE. Some across clues cross the two-possibility squares, and these clues have 2 answers depending on the outcome of some event. For example, 23 Across "Presidential election winner" solves to JOSEPHBIDEN / DONALDTRUMP, like the famous CLINTON / BOBDOLE crossword. This represents multiverse travel, and we indicate these with cyan backgrounds in what follows.

• Finally, some entries make more sense if we interpret them within a specific year. For example, 52 Across "Sticky paper that went on sale recently" solves to POSTIT, which was first widely sold in 1980. These represent time travel. Each grid is from a different year (1980, 2008, or present), and this gives a way to order the grids. Each grid has at least 1 multiverse entry that makes the most sense in that year.

  These entries are highlighted in purple backgrounds in what follows.

In what follows, we also use yellow backgrounds for crossword entries related to chess; more on that later.

1980 crossword

Fill

Across clues

Down clues

2008 crossword

Fill

Across clues

Down clues

Present crossword

Fill

Across clues

Down clues

Rules of 5D Chess

Now it's time to learn how to play 5D Chess! Hopefully we have sent some teammates to learn the rules of 5D Chess while working on the crossword. (If we are anything like teammate's testsolvers, we did not do this.)

Good resources for this are:

• a Steam tutorial on piece movement
• Gameplay videos from content creators
• Guides for the in-game puzzles that are designed to teach game rules
• and the 5D Chess wiki

Here are the rules relevant to the puzzle:

Piece movement / board reading

Pieces lie in 4D space, corresponding to (timeline, time, file, rank). File and rank are from 2D chess, timeline is vertical time, and time is horizontal time.

In the puzzle, only kings, bishops, and knights are used. Kings can move 0 or 1 in any number of dimensions. Bishops can move exactly N squares in exactly 2 dimensions. Knights can move exactly 2 squares in 1 dimension + 1 square in a 2nd dimension.

In 5D Chess, the purple arrow under the grids represents the flow of time. A timeline is a series of boards in a single row. Whenever a "normal" play (no time nonsense) is made, a new board is added to the timeline.

The color of the outer border denotes whose turn it is. Boards in 5D Chess are immutable, and pieces can only move from the latest board in each timeline (usually called the active board). The active board gets a thicker border.

Normally, borders in 5D Chess games alternate white - black - white along a timeline, since moves alternate white / black / white. Each (white+black) pair corresponds to 1 distance in time, and a piece can only time travel to a board with the same color border (to a board where it was their turn.)

In this puzzle, we play as white, and the black bordered boards are omitted. Taking the 3rd example, it is a 5D Chess position with 1 timeline, 3 timesteps, where only the B and N on the last board are movable, since the rest are inactive.

Checkmating

Checkmating is similar to 2D chess: if a player has no move that can stop a piece from capturing a king, then that player is in checkmate.

Kings in 5D Chess can move in 4 dimensions, giving up to 80 different moves, making it very hard to mate a king on an active board. (It's possible, but hard.)

However, on past boards, no pieces can move, because history is immutable. So, any piece that attacks a past king checkmates that king, unless the other player can stop the attacking piece.

This is the mate used in this puzzle.

For example, take the first example from the puzzle page.

In this example, moving the knight to a green square is a mate, because doing so will add a new board, as shown below.

Now the knight is attacking the king 1 timestep ago on a1, with (T2) Nc1 to (T1) Na1. The black king cannot capture the knight in 1 move, so it is mated.

However, consider the second example from the puzzle page.

The same move does not work, because the black king on b2 can take the knight, stopping the mate.

So, the green squares represent checkmates.

Branching

So far, we have only described moves that do not time travel. For the last example, that's about to change.

Since boards are immutable, when a player moves a piece back in time or across timelines, it branches a new timeline. Timelines are created downward from the perspective of the current player. Since we are playing as white, black branches are added upwards, and white branches are added downwards.

Branching counts as making a move in both the source and destination timeline, giving the turn to the other player.

In this image, it is black's turn. The knight in the topmost timeline branches by travelling to the middle timeline. In the top timeline, the next board is white's move without the knight.

In the newly created timeline, it is also white's move, with an extra knight on the board.

(Note that the topmost timeline was created by white branching via a bishop moving from the middle timeline last turn.)

Finally, in 5D Chess, 1 move can be made of multiple submoves, up to 1 per active timeline. The exact rules of this are both a bit complicated and not relevant to the puzzle, since all extraction is based moving exactly 1 piece.

Those interested in the extra cases can go to the Appendix.

Solving the chess problem

Here are all the chess-based clues from the earlier crossword.

The boards can be ordered based on their year (1980 - 2008 - present). We should ignore rooks and pawns, treat all Ks as kings, Js as knights, and Bs as bishops.

We could interpret the multiverse entries in two ways: either there are 2 timelines, with 1 prime timeline + 1 branch, or 4 timelines, with 1 prime timeline + 3 branches.

Since there are 2 grids with movable pieces, and 55 says "the branch", it is more consistent to use a 2 timeline setup, where the timeline with alternate entries was created by black many moves in the past.

This gives the following grid (click to enlarge):

By convention, the original timeline is L0, white timelines are L1, L2, ..., and black timelines are L(-1), L(-2), etc. We follow this convention, so the puzzle starts with L0 and L(-1).

Since only pieces on active boards can move, we only need to consider the movements of 4 pieces, the bishop on L(-1)T3, and the 2 knights and 1 bishop on L0T3; these are highlighted in color in the figure above.

The position of the kings in (x,y) space will never change; only distances in (L,T) space will change, depending on which board we move to. So, we will often use the following figure, which shows the projection of every black king onto (x,y) space.

At a high level, the way we check all cases for checkmate is to

1. See where the board will be created in (L,T) space.
2. Project all kings onto the (x,y) dimension on the new board.
3. Mark all moves that can end up on this board.
4. Use the projected-kings view to check which moves can attack a past king.
5. Verify those moves cannot have their checkmate interrupted.

There are a few ways to split up the case checking. We could do it piece-by-piece based on movable pieces, or king-by-king to check where each king could be mated from, or board-by-board based on where new boards will be added.

For this solution, we'll do it board by board.

Case 1: Moving to L(-1)T3

A board will be created at L(-1)T4 if a piece from L(-1)T3 moves to its own board, or a piece from L0T3 moves to L(-1)T3. (This second case does not create a branch because both the source and destination boards are active - for simplicity these moves do not contribute to extraction to avoid needing to understand this rule.)

In general 5D Chess, attacking a past king from T4 may not be checkmate if there are 2 active timelines, even if the attacking piece cannot be taken. This is because a player that would be mated could create a new timeline to prevent the checkmate move from occurring.

For more explanation, see the appendix, but the short version is that in this particular setup, that trick does not work, attacking from T4 will always be a mate if the attacking piece can't be taken, and if we never find this edge case we can still solve the puzzle.

Here is a display of all possible moves to the L(-1)T3 board. Squares for the pieces original location are labeled with which board they came from.

From the new board in L(-1)T4 to each of the six existing boards:

• The king in L(-1)T1 (cell l13) can be attacked by a bishop 3 cells away (in one orthogonal direction).
• Kings in L0T1 (cells l6 and l13) cannot be attacked by a knight or bishop.
• The kings in L(-1)T2 (cells c7, g9, i9, and m5) can be attacked by a knight 1 square away, or a bishop 2 cells away.
• Kings in L0T2 (cells c7 and m5) can be attacked by a knight in the same cell.
• The king in L(-1)T3 (cell e4) can be attacked by a knight 2 squares away or a bishop 1 square away.
• The kings in L0T3 (cells b3 and e4) can be attacked by a bishop on the same cell.

Also, on this board no check is possible on the board (-1)T4 itself.

There are two moves that result in a check to a past king, by moving the bishop from L(-1)T3 to either e5 and f4. These moves are circled above.

However, neither of these are mates, because the black king on L(-1)T4 can then capture the attacking bishop, which is not guarded by any other active piece. Hence in both cases, the diagram above has "NG" written ("no good") to indicate that the check does not lead to mate.

Hence, no checkmates arise from this case.

Case 2: Moving to L0T3

Add moves in a similar way as Case 1, and look for checks. This time, both the knights as well as the bishop from L0T3 can deliver checks.

The moves to a3, b4, c4 are not checks because the active king on L0T4 can capture the attacking piece. The other four moves (knight to c8, knight to g4, or bishop to either e7 or c5) are both checkmates (denoted "OK" in the diagram).

Case 3: Moving to L(-1)T2

Based on the branching rule, this will create a copy of the L(-1)T2 board at L1T3, with the extra piece.

We consider each move - note there are not many moves to this board because the knights on L0T3 cannot reach L(-1)T2 at all.

We also now need to consider any pieces that may exist on the board that we branch to - these pieces cannot move right now, but will be active on the next move, so they can contribute to checkmates. (This realization will be important later.)

Considering each king in turn, highlight all attacked kings. This time it's fairly easy because a bishop can only attack a king that is 2 dimensions away, so most kings are irrelevant, aside from the kings in the bottom left that are 0 away in one coordinate.

There is only one check, when the bishop moves to g4. This move is a checkmate since it does not border any active king.

Case 4: Moving to L0T2

This is similar to the previous case, except with more moves to consider since the knights on L0T3 can reach L0T2.

Once again filter to squares where a piece can attack the king. There are only one plausible square: the knight jumping to e5, attacking the e5 king in L0T2.

This move is not a checkmate because the king on L0T4 can then capture the attacking knight.

Hence there are no checkmates in this case.

Case 5: Moving to L(-1)T1

The branching rules will create a copy of the L(-1)T1 board at L1T2.

Before considering the moves that can reach this board, consider the knight at L1T2 on cell i8 that's made from the branch. This knight will be active in the new branch, and is already attacking the king at L(-1)T2 on cell i9.

Since it is not neighboring any active king, this knight is checkmating black, no matter what additional piece moves to this board. This is the key a-ha needed for the chess problem, since it contributes most of the letters of the extraction phrase: Every move to L(-1)T1 is a checkmating move.

Note that one square is reachable by 2 pieces, but it is only used once in the extraction since we count by number of checkmate squares, not number of checkmate moves.

Case 6: Moving to L0T1

This also creates a board at L1T2. Since there is a knight on the L0T1 board in the same i9 position as Case 5, this case works identically: any move that branches to L0T1 is a checkmate.

The possible moves are drawn below.

Combining all cases

Reading the extraction letters in order of the boards gives FIRST OF NINETY FIVE POEMS.

95 Poems is a poetry collection by e.e. cummings.

If we find a table of contents for the book (i.e. OpenLibrary and click Preview, or Google Books), we find the first poem is l(a. The answer is the full text of the poem:

l(a

le
af
fa

ll

s)
one
l

iness

Authors' Notes

In some ways, this puzzle was over 2 years in the making. I got the idea from a joke DP Puzzle Hunt team name, went "haha that's funny", and filed it away in my puzzle ideas doc.

Shortly after we won Mystery Hunt, I looked through my old ideas, and tried to more seriously come up with what a "5D Crossword with Multiverse Time Travel" would look like. That landed on the Clinton/Bob Dole crossword, with more escalation - the original prototype tried to make the multiverse entry be "Presidential Election winner" in all 3 grids in the same position. It's possible if you really stretch things - tons of candidates have 11 letter full names. But it relied on dipping into 3rd party candidates and it didn't feel like the added constraint did enough work for the puzzle.

The 1st prototype used a placeholder extraction and went over well. When deciding how to evolve it into a larger puzzle, the editors and I tossed around a few ideas, and decided the most exciting approach would be to use 5D Chess With Multiverse Time Travel for real.

This ended up taking several weeks of my life, because neither I nor the editors had actually played 5D Chess. I first had to buy the game to teach myself the rules, understand an incredibly long maze of edge cases, then figure out which edge cases I wanted the puzzle to rely on (the answer was "not many"). Many of these edge cases were only found after I built the entire chess position and crossword fill, and one was only found after testsolving finished. I got quite lucky that none of them impacted correctness, they just made the full analysis 2x longer.

The first few testsolves of the chess step were a disaster, where solvers would believe they understood 5D Chess without actually understanding 5D Chess. The examples were added to encourage solvers to learn the correct rules. We wanted to hide the parallel timeline a-ha for the crossword as much as possible, so all examples were deliberately 1 timeline only, relying on just 55-across to nudge towards the correct interpretation of how branches work in 5D Chess.

The final chess setup is built partly via script and partly by hand. It is close to the minimal number of chess pieces needed to extract 22 squares - the trick with branching to T1 was done primarily because not doing it would force solvers to consider the moves of around 10-15 chess pieces rather than just 4. Testsolvers seemed to like that trick after they got it, so all's well that ends well.

At some points, I was not convinced this puzzle should even exist, but editors and testsolvers encouraged me to finish it, saying it was "exactly the bullshit I expect to see in Mystery Hunt". (The lucky postprodder for the puzzle would also like to voice his support.) Hope you had fun! Really, it could have been much worse.

Appendix

What follows is a list of edge cases that are part of the rules, but which we decided were too complicated for the puzzle. We did our best to guide solvers to the puzzle solution before they could think of these edge cases.

The Present and submoves

The Present is denoted by a vertical bar, and is placed at the earliest active board among all timelines.

In 5D Chess, the exact definition of a move is "a player moves any number of pieces from active boards, until the Present switches to the opponent"

If there are 2 active timelines, then 1 move can involve moving 2 pieces normally, to advance the Present 1 step forward.

But it could also mean only moving 1 piece, to move the Present back in time, like the knight is doing here.

White can move a piece in the top timeline, but doesn't have to move a piece in the top timeline, because whether they do or not, the Present has already passed to the opponent.

Technically, in the cases where we move entirely within 1 timeline without time travel or branching, we also needed to make an arbitrary submove in the other timeline to pass the Present. We ignored this for extraction because that other submove is unconstrained.

General note on game diagrams

All images from the game are generated via GHXX/FiveDChessDataInterface/ (thanks to the 5D Chess Discord for helping me with installation)

This mod allows you to load game positions, with some constraints: your position must alternate white / black / white / black, and you can use a board size of at most 8x8.

We've aimed to use in-game diagrams as much as possible in this Appendix, but in some situations we need the full 13x13 board and will revert to the earlier format.

When there are 2 timelines, why are some attacks on past kings not checkmates?

Consider the following innocuous example, based on the 1st example, except with 2 timelines and with an extra timestep of padding.

We make the same checkmating move as before.

This is not a checkmate for black! They can pull a pro Sans Undertale move. A checkmate is defined as "a piece would take the king on the next move", but white can't take a piece if it's not their turn.

Black branches from the 2nd timeline, creating this board state.

This passed the present to white, so it's a valid move. In the middle timeline, it it still black's turn, so white cannot move the knight to take the king. Black has avoided getting mated in one.

The reason this doesn't matter for the 1 timeline case is that black branching back in time counts as making a move in the timeline you move from, which passes the turn to white and lets the mate happen.

The trick is only possible if the defending player can branch from a timeline without the attacking piece.

5D Chess would be pretty degenerate if you could do this forever, so 5D Chess comes with extra rules about timelines.

• The game tracks how many timelines each player has created, starting at 0 for both.
• A player can go to -1, 0, or +1 timeline advantage without issue.
• However, if a player creates at least 2 more timelines than the other player, the new timeline is inactive and will not move The Present.

Continuing the example from earlier, after white makes any move, the game is over, because black is already at +1 timelines, so the 2nd timeline cannot move the Present back in time.

What happens if black attempts to Sans Undertale again? The new timeline has a black arrow under it instead of a purple one - this indicates the timeline is an inactive timeline made by black which will not move The Present.

This is why the original position is set up with black creating a branch many moves in the past, even though it is less intuitive to place the alternate timeline above the true timeline. Doing so limits black's defensive options. In 5D Chess, creating more timelines than the opponent is usually bad. A player has timeline advantage if they have created 1 fewer timeline than their opponent, and timeline disadvantage if they have created 1 more.

By starting black at a +1 timeline disadvantage, if white does not branch, black cannot stall by branching, since black's new timeline would be inactive and not move The Present. Solvers can safely solve the puzzle even if they don't realize this edge case exists.

But what about the moves where white branches? That puts black's timeline advantage back to 0, can't they pull a pro Sans Undertale move in that case?

Here is a small reproduction of the scenario where white can checkmate while going back from time t to time t-1.

If black wants to try delaying the mate, they can only do so from the original timeline at t+1, or the new timeline at time t. Moving from the new timeline does not work because it will pass the turn to white on that timeline. Moving from the original timeline will not work because kings can only move back one square in time, going from t+1 to t, which does not move the present.

So, in short, nope! It really does not matter! All this timeline nonsense can be ignored.

Showing we cannot mate an active king

It is generally not possible to constrain all moves of an active king with the pieces we have. However, in 5D Chess a board can have multiple kings, and it might be possible to fork 2 active kings.

If 2 active kings can be forked and the attacking piece cannot be removed, then it is a mate. The same is true if we pin a king behind another king.

To show this is not possible, we consider each board with at least 2 kings, and show there is no way to place a piece to cause such a fork or pin.

Any of the boards with 2 kings could become an active board if we branched to that board, so we must check all boards. However, it is enough to only check for non time-travel attacks, since all attacks on past kings are covered by the earlier parts of the solution.

Case 7: Fork on L0T1

There is no way to attack both kings with a single knight or a single bishop.

Case 8: Fork on L(-1)T2

Here is the board from earlier with all fork positions marked.

Of the possible moves on this board, the only one that forks two kings is the bishop at i10. We already saw the black king can just capture this bishop.

Case 9: Fork on L0T2

There is no overlap between the fork cells and the possible movement cells (although it is close, just 1 square away).

Case 10: Fork on L0T3

There is no overlap between the fork cells and the possible movement cells, although again it is quite close.

Remaining cases

Finally, we should consider the case where we fork 2 active kings across 2 active timelines. This is not a checkmate because if both timelines are active, the opponent may make a move in both of those timelines on their turn.

So it is enough to check cases within just a single board.

Showing there are no mates relying on moving 2 pieces

There are a few options that open up if we consider moving 1 piece from both active timelines.

Branching twice by moving 2 pieces back in time

We can travel back in time from both active timelines - the 1st will create a branch at L1, and the 2nd will create a branch at L2.

So for each case based on branching, we should consider if we have new mates that exist if we are an extra timeline away, at L2 instead of L1. We can reuse the board analysis from before, labeling the kings as 1 further away in timeline space.

For moves to T1, we already know all moves to that board are checkmates, so we can ignore them.

Case 11: For L(-1)T2

There is no such move - the only possibility is getting a bishop to L2T3 g4 to attack the king at L0T3 e4, but this would produce the same checkmate square as bishop to L1T3 g4, which we've already found from a 1 piece mate.

Case 12: For L0T2

For L0T2, there is a move that looks promising:

Earlier, we concluded that knight to L1T3 e5 attacking a king at L(-1)T3 e4 was not a valid checkmate, because it could be taken by another king at L0T4 e4.

However, if we first create a buffer timeline, we could get a knight to L2T4 e5, which still attacks a king at L0T3 e4,4, but is now out of reach of the king at L0T4 e4.

This is not a checkmate because it acts like the softmate from the previous appendix.

Doing this move must create 2 active timelines, the buffer timeline (with no mate) and the attacking one (with pending mate). White made both timelines, so black's timeline disadvantage goes from +1 to -1.

This means if black branches, the timeline will be active, which will shift the present back, letting black leave the 2nd timeline in a not-your-turn state. (This timeline does not have a previous black board, but it is 1-away from a timeline with longer history that we can still reach.)

What if white creates 2 branches where both branches would be checkmate?

In that scenario, black would have no way to delay both mates, because black would not have a free timeline to branch back from, leaving them in checkmate.

Here is a concrete example from the given board state: the bishop from L(-1)T3 mates by going to L(-1)T2, and then the knight from L0T3 mates by going to L0T2.

This is a checkmate for black, but the checkmate from the knight in L0 only exists because we 1st checkmated via the bishop from L(-1). We must play the knight move after the bishop move to make the timeline positioning work. By the time we can play the knight checkmate, we have already won and are just playing extra moves for no reason.

It's slightly ambiguous whether this should count for extraction, but given that it relies on making moves after the game is in an already-won state, we consider it as invalid for the puzzle.

Make a regular move, then branch to T3 with the 2nd piece

This is the last edge case!

Suppose we made a submove in one timeline that did not time travel, say from L(-1)T3. Then we moved a second piece from L0T3 to L(-1)T3.

Since we've made a move at L(-1)T3 already, we are now moving to a past board, and this will create a branch at L1T4.

We therefore need to check the moves for L(-1)T3 to L0T3 and L0T3 to L(-1)T3 to check that there is no extra mate created by this case

Case 13: Making a move on L(-1)T3 then moving from L0T3 to L(-1)T3

The timeline looks as follows.

We draw the possible moves that could cause this; note that this is almost the same figure as Case 1 except the bishop at i10 does not have moves.

None of the moves can attack a past king.

Case 14: Making a move on L0T3 then moving from L(-1)T3 to L0T3

The timeline looks as follows.

None of the bishop moves are able to attack a past king.

This finishes the "move two pieces" analysis. Phew!