Death Match 4: Buck Konundrum

In Buck Konundrum, players have to evaluate what a set of bizarre, Duck Konundrum-style steps do to their bucks and count up the money they have at the end.

RULES

This Death Match consists of a number of puzzles, grouped into several rounds.

The rules for a single puzzle are described below.

A puzzle presents you with an inventory and a list of steps. The inventory consists of a number of banknotes of a variety of denominations. Each step in the list is a command that you must follow; generally, steps manipulate the contents of your inventory.

The answer to a puzzle is determined as follows. First, follow the list of steps in order from top to bottom. Then, count up the amount of money in your inventory; each banknote of a denomination is worth that many dollars. Your answer is this final amount of money.

There are some terms that are often used in the steps; these terms are given in a glossary given at the end of these rules.

To see an example puzzle, check out the example round given at the end of these rules.

The rules for the actual game are described below.

The game is divided into 4 rounds. Each round runs for 10 minutes.

In each round, there are a number of puzzles presented at the same time. The rounds have a fixed structure given at the end of these rules.

The format of these puzzles is as follows. All puzzles in a round have a common inventory. In addition, there is a big list of steps. Each puzzle starts their list of steps from a specific point of the big list and goes until the end of that big list. See an example round given at the end of these rules.

Although the puzzles in a round have a common inventory and share a lot of steps, they are completely independent. What you do on a puzzle does not affect any other puzzles in a round.

Once the round appears, you will race against your opponent to solve the puzzles. You may solve the puzzles in any order you wish.

To submit an answer, simply indicate the puzzle (with either its color or its number) and its answer (the amount in $; you don't have to put the $). After you submit the answer, you will know whether your answer is correct or not. (Allow a few seconds as the host will manually check the answer.)

If your answer is correct, you score a number of points. The number of points is equal to the number of steps in the puzzle; for example, a 3-step puzzle is worth 3 points. The points are only awarded to one player; once you solve a puzzle, your opponent cannot solve it as well.

There is no specific penalty for an incorrect answer. However, at the start of the round, you may make 1 guess for each puzzle. Every 3 minutes (3:00, 6:00, 9:00), you receive 1 additional guess for each puzzle. If you have no guesses for a puzzle, you may not answer for it; any attempt to answer it will be ignored.

To emphasize once again, puzzles in a round are completely independent. The number of guesses you have for each puzzle is separate and doesn't affect the other puzzles.

The round ends once all puzzles have been answered correctly or 10 minutes have elapsed (or both players are locked out from all remaining puzzles).

The game goes for 4 rounds. At the end of the 4 rounds, the player with the most points wins.

In case of a tie, a tiebreaker round will be played, consisting of only one puzzle. The player that answers this puzzle correctly wins; in case time runs out with both players unable to answer, the DM Opponent wins.

APPENDIX

Structure of the rounds

Each round consists of puzzles with the following number of steps:

• Round 1: 3 steps, 4 steps, 5 steps (total 12 points available)
• Round 2: 4 steps, 5 steps, 7 steps (total 16 points available)
• Round 3: 4 steps, 6 steps, 8 steps, 9 steps (total 27 points available)
• Round 4: 5 steps, 7 steps, 9 steps, 11 steps, 12 steps (total 44 points available)
• Tiebreaker: 7 steps

Example round

Check the following thread for an example round and explanation for the answers.

There are 3 puzzles: a 3-step puzzle (marked red), a 5-step puzzle (marked blue), and a 6-step puzzle (marked green).

🔴 For the red puzzle, the list of steps is:

1. Receive a $2 banknote for each set of 3 $1 banknotes.
2. Exchange each $5 banknote for a $10 banknote.
3. Forfeit each banknote of the highest denomination you have.

Your inventory starts as: 4 x $1, 3 x $5, 2 x $10, 1 x $20.

After step 1, you receive 1 x $2 (your $1 banknotes form one set of 3; the extra one doesn't make a set). Your inventory is now: 4 x $1, 1 x $2, 3 x $5, 2 x $10, 1 x $20.

After step 2, you exchange 3 x $5 for 3 x $10. Your inventory is now: 4 x $1, 1 x $2, 5 x $10, 1 x $20.

After step 3, the highest denomination you have is $20, so you forfeit 1 x $20. Your inventory is now: 4 x $1, 1 x $2, 5 x $10.

The total worth of banknotes you have, and so the answer, is $56.

🔵 For the blue puzzle, the list of steps is:

1. Exchange each $20 banknote for 20 $1 banknotes.
2. Delete the 5th step from top.
3. Receive a $2 banknote for each set of 3 $1 banknotes.
4. Exchange each $5 banknote for a $10 banknote.
5. Forfeit each banknote of the highest denomination you have.

Your inventory starts as: 4 x $1, 3 x $5, 2 x $10, 1 x $20.

After step 1, you exchange 1 x $20 for 20 x $1. Your inventory is now: 24 x $1, 3 x $5, 2 x $10.

After step 2, step 5 is deleted. The list of steps is now:

1. Exchange each $20 banknote for 20 $1 banknotes.

> 2. Delete the 5th step from top.

1. Receive a $2 banknote for each set of 3 $1 banknotes.
2. Exchange each $5 banknote for a $10 banknote.

After step 3, you receive 8 x $2. Your inventory is now: 24 x $1, 8 x $2, 3 x $5, 2 x $10.

After step 4, you exchange 3 x $5 for 3 x $10. Your inventory is now: 24 x $1, 8 x $2, 5 x $10.

Step 5 was deleted earlier, so you don't do it.

The total worth of banknotes you have, and so the answer, is $90.

🟢 For the green puzzle, the list of steps is:

1. Insert the step "Exchange each banknote of even denomination for a banknote of half that denomination" to after the 5th step from top.
2. Exchange each $20 banknote for 20 $1 banknotes.
3. Delete the 5th step from top.
4. Receive a $2 banknote for each set of 3 $1 banknotes.
5. Exchange each $5 banknote for a $10 banknote.
6. Forfeit each banknote of the highest denomination you have.

Your inventory starts as: 4 x $1, 3 x $5, 2 x $10, 1 x $20.

After step 1, you insert a new step; this takes place between what's currently step 5 and step 6. The list of steps is now:

> 1. Insert the step "Exchange each banknote of even denomination for a banknote of half that denomination" to after the 5th step from top.

1. Exchange each $20 banknote for 20 $1 banknotes.
2. Delete the 5th step from top.
3. Receive a $2 banknote for each set of 3 $1 banknotes.
4. Exchange each $5 banknote for a $10 banknote.
5. Exchange each banknote of even denomination for a banknote of half that denomination.
6. Forfeit each banknote of the highest denomination you have.

After step 2, you exchange 1 x $20 for 20 x $1. Your inventory is now: 24 x $1, 3 x $5, 2 x $10.

After step 3, step 5 is deleted (this is the one just above the new step). The list of steps is now:

1. Insert the step "Exchange each banknote of even denomination for a banknote of half that denomination" to after the 5th step from top.
2. Exchange each $20 banknote for 20 $1 banknotes.

> 3. Delete the 5th step from top.

1. Receive a $2 banknote for each set of 3 $1 banknotes.
2. Exchange each banknote of even denomination for a banknote of half that denomination.
3. Forfeit each banknote of the highest denomination you have.

After step 4, you receive 8 x $2. Your inventory is now: 24 x $1, 8 x $2, 3 x $5, 2 x $10.

What was originally step 5 was deleted, but there was also a new step inserted right after the original step 5.

After this step 5, you exchange 8 x $2 for 8 x $1, and 2 x $10 for 2 x $5. Your inventory is now: 32 x $1, 5 x $5.

After step 6, the highest denomination you have is $5, so you forfeit 5 x $5. Your inventory is now: 32 x $1.

The total worth of banknotes you have, and so the answer, is $32.

In summary:

• The 3-step red puzzle has answer $56.
• The 5-step blue puzzle has answer $90.
• The 6-step green puzzle has answer $32.

Glossary

Check the following thread for a glossary of terms you will often find in the steps, to know their exact definitions.

Banknote, denomination: A banknote is an object you have in your inventory. It has a denomination, which is a dollar value. All denominations are guaranteed to be positive integers; you will not have to involve banknotes with denomination $-1, $2.5, or $0. However, denominations don't have to be "nice" numbers; they do not necessarily exist as U.S. dollar denominations or any other currency, and you may have to deal with $47 banknotes.

Worth: The total worth of some collection of banknotes is the sum of all their denominations; if multiple banknotes have the same denomination, count the denomination as many times as there are banknotes. The answer to a puzzle is just the total worth of all banknotes you have after performing all the steps.

Each, all: "Each" and "all" generally mean "every" in English. The main difference is "all" takes everything into a single command while "each" makes separate commands. For example, if you have three $1 banknotes, "exchange each $1 banknote for a $2 banknote" gives you three $2 banknotes, while "exchange all $1 banknotes for a $2 banknote" only gives you one $2 banknote.

Set: A set contains the banknotes indicated. Sets are never partial; if there are not enough banknotes, they don't form a set. For example, if you have 5 $1 banknotes, "each set of 2 $1 banknotes" refers to two sets of 2 $1 banknotes; there is a leftover $1 banknote that doesn't form a set.

Receive: Receive means you get new banknotes. If this depends on other banknotes you have, you don't forfeit the other banknotes. For example, "receive a $2 banknote for each $1 banknote" gives you $2 banknotes but doesn't take away your $1 banknotes.

Forfeit, exchange: Forfeit means you lose some banknotes you have; exchange means you forfeit some and receive some. It is guaranteed that you will not be told to forfeit more than what you currently have; for example, if you only have two $1 banknotes and you need to do "forfeit 3 $1 banknotes", you have done a mistake. (But you might be instead told to do "forfeit all $1 banknotes", then you forfeit your two $1 banknotes.)

Step from top/bottom: These terms are used to refer to a specific step. Note that the step number from the top will change depending on the puzzle. All references are guaranteed to be valid; if a puzzle contains 4 steps, it will not refer to "the 5th step from top".

Insert, delete: Insert means to write a new step at a given position; the position is always given as "after X step", meaning directly after the indicated step. Delete means to erase a step at a given position. It is guaranteed that adding and deleting only occurs to steps that are after the currently performed step; if you are currently doing the 3rd step from top, you will not delete the 2nd step from top.

Swap: Swap means to exchange the positions of two rules in the list. Unlike inserting and deleting, swap may involve steps before the currently performed step, although it will not involve the current step. Steps swapped to above the current step will not be performed (unless it's swapped back down, of course); steps swapped to below the current step will be performed again later.

ADMINISTRATION

Timing

This game runs in real time. Each round lasts 10 minutes, but you may answer any time you are allowed to.

Submissions and allowed tools

All submissions are done publicly in the game room.

You may use any available tools for note-taking. However, you may not talk to other people or use any automated programs. Specifically, you may not use any calculator.

Information

All information in this game is public, with the obvious exception of the rounds you haven't seen.