Parlor Game
Spoilers Ahead
This page contains spoilers for solving Parlor Games. View at your own discretion.
The Parlor Game is a puzzle in Blue Prince. Found in the Parlor, the puzzle consists of three sealed boxes each labelled with statements and a Wind-up Key found on the desk. The player must determine which of the three boxes contains the "prize" and open it with the one-use Wind-up Key.
The "prize" box contains two gems, whose color depends on the box they are found in: blue for the blue box, yellow for the white box, and pink for the black box. Opening a box other than the prize box has no effect and wastes the key.
Although there is always at least one statement pertaining to the location of gems, technically no gems exist until the prize box is opened, which spawns the gems in. If an empty box is opened quickly followed by the prize box, then no gems will spawn, possibly due to a bug.
For a complete list of all possible Parlor Games along with their solutions, see /List of Parlor Games.
Parlor Game basics
The Parlor Game is an exercise in pure logic. All three boxes have some number of statements on the top, some of which are true and some of which are false. There will always be at least one statement will hints towards the location of the prize. It is always possible to precisely determine which box contains the prize using just logical deduction, the boxes and their statements, and the Parlor Game rules:
Rule 2: There will always be at least one box which displays only false statements.
Rule 3: Only one box has a prize within. The other 2 are always empty.
Parlor Game - Basic example #1
The boxes read as follows:
The blue box statement is obviously true, and the white box statement must also be true due to Rule 3. According to Rule 2, there must be a box with false statements, so the black box is false by elimination. Hence the black box is not one of the two empty boxes, i.e. the black box contains the prize.
Parlor Game - Basic example #2
The boxes read as follows:
The blue statement and the white statement are functionally saying the exact same thing, so they share a truth value. All statements point to the black box - but this can't be the case, as Rule 2 says there must a box with false statements. Similarly, the gems cannot be in the white box, as then every box would be false, violating Rule 1. The only remaining possibility is that the gems are in the blue box.
Parlor Game - Basic example #3
The boxes read as follows:
Here the white box statement copies the truth value of the black box, and the blue box has the opposite truth value. So there are only two cases to consider:
1) The black box is true, making the white box true and the blue box false. A false box contains the gems, and the blue box is the only false one, so the gems are in the blue box.
2) The black box is false, making the white box false and the blue box true. A true box contains the gems, and the blue box is the only true one, so the gems are in the blue box.
Both cases obey all three rules, so there is no way to distinguish which case is valid. But it does not matter, as they both place the gems in the blue box. Thus it is still possible to locate the gems when the truth value of some or even all of the boxes is indeterminate.
Increasing difficulty
If you've found a new clue, you know what to do.
Do Parlor Games necessarily need to be solved correctly for the difficulty to increase?
As Parlors are drafted and Parlor Games are attempted, the difficulty of future Parlor Games increases, gradually but permanently. Initially, the increases will be subtle, with knottier logic and fewer boxes containing trivially true/false statements. But eventually the Parlor Games will be complicated in other ways:
- Strange statements: Subjective and/or prospective statements may appear with the goal of confusing the player, such as "YOU WILL NOT SOLVE THIS PUZZLE" or "YOU WILL OPEN THIS BOX AND FIND IT EMPTY". These statements are actually much nicer than they look, as they are always either irrelevant or capable of being evaluated based on the surrounding statements.
Parlor Game - Intermediate example #1
The boxes read as follows:
The black box and the blue box are functionally saying the exact same thing, so they share a truth value. Because the boxes cannot be all true or all false, the white box must have the opposite truth value. Thus, knowing the white box's truth value solves the puzzle. If it were true, we would know the truth value of every box, despite the white statement asserting that it is of no help - a contradiction. So the white statement must be false, which is helpful indeed as it makes the other two statements true and puts the gems in the blue box.
- Blank boxes: Sometimes, one box may have no statement at all. Mathematically inclined players may assume that a blank box vacuously satisfies both Rule 1 and Rule 2 by itself; however, there must be two boxes with one or more statements that are all true and all false respectively. As such, a blank box satisfies neither Rule 1 nor Rule 2, and implies that one of the other boxes is all true and the other is all false.
Parlor Game - Intermediate example #2
The boxes read as follows:
As the white box is blank, it is neither all false nor all true, going by Parlor Game convention. As such, one of the other boxes must be true, and the other false.
Notice that the blue statement implies the black statement. If the blue statement is true and the gems are in the black box, then they are in a box with a statement, making the black box true as well. But that leaves no false box, so this is impossible, meaning the blue statement is false. Now the black statement must be true by elimination, meaning the gems are in a box with a statement other than the black box: the blue box.
- Ambiguity Rule: Some Parlor Games may require invoking an additional unstated rule: The valid truth assignments for statements must unambiguously define a specific box to contain the gems.
Parlor Game - Intermediate example #3
The boxes read as follows:
This puzzle can be solved easily by noticing that the truth values of all statements would not change if the gems were moved between the Blue and Black boxes, meaning it would be ambiguous unless the gems were in the White box.
However, if trying to solve without invoking this rule, a valid truth assignment would making the blue statement false and the white/black statements true:
- To have the white statement be true, the gems must be in either the blue or black box.
- The black statement is true as "BOTH OF THE OTHER BOXES CONTAINS GEMS." is obviously false and "BOTH OF THE OTHER STATEMENTS IS FALSE." is false due to the black box being true.
However, this truth assignment ambiguously places the gems, and hence is invalid.
- Multiple statements: Further into the Parlor Games, multiple statements may be found on one box. It now becomes possible for a box to be neither all true nor all false, though it's impossible for multiple boxes to be in this state due to the rules. Once a large number of Parlor Games have been completed, there can be up to three statements on each box, even resulting in Parlor Games involving nine statements.
Parlor Game - Advanced example
The boxes read as follows:
THE GEMS ARE IN A BOX WITH A TRUE STATEMENT
THE GEMS ARE IN A BOX WITH TWO STATEMENTS.
THE GEMS ARE IN A BOX NEXT TO THIS BOX.
THE GEMS ARE IN A BOX WITH THREE STATEMENTS.
THERE ARE THE SAME NUMBER OF TRUE AND FALSE STATEMENTS ON BOXES.
With eight total statements, none of which are trivial, this Parlor Game is a genuine challenge. There are many approaches to solve it, but here is one:
Note that the first statement of the blue and black boxes both imply that each of those boxes must have a false statement. In both cases, either the top statement is false, or it is true and another statement on the box is false. Either way, the blue box and the black box must both have at least one false statement. That means, according to Rule 1, that the white box must be all true statements. Unfortunately, all that says currently is that the gems are either in the black box or the blue box.
Continuing, the black box's second statement is true: the gems are in the blue box or the black box, both of which have three statements. So both the white box and the black box have a true statement, meaning that the blue box must be entirely false according to Rule 2. The blue box says that the gems are in a box with a true statement: as this is false, the gems must be in a box without a true statement. The only box without a true statement is the blue box, so the gems are there.
More can be done to determine the truth values of all eight statements, but this is not necessary.
A grander prize
Spoilers Within
This section contains spoilers for advanced Parlor Game rewards.
The 40th prize box opened will also produce A Logical Trophy.