# Digital root

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A **digital root** is the result of finding the sum of several digits until there is only a single digit remaining. Digital roots play a huge role in the Nonary Game in *999*.

Examples:

- 1234: 1+2+3+4=10, 1+0=1. The digital root of 1234 is 1.
- 678: 6+7+8=21, 2+1=3. The digital root of 678 is 3.

## Nonary Game

In the Nonary Game, digital roots are the keys to escape. Certain doors on the ship contain numbers painted on them in red paint. These numbered doors can only be opened when the numbers of bracelets verified have a digital root of that number. If the digital root of these numbers is not the number on the door, the RED will read "ERROR" and the screen will clear.

## Number 9

In the Nonary Game, the number 9 is an extremely valuable and versatile number, as it is the only number that will not change the digital root of the number(s) it is added to. This means that the bearer of the number 9 bracelet can more easily control their fate than the other players, as they can join any team whose digital root is 9, even teams of two. The only character who has a bracelet that displays the number 9 is Teruaki Kubota. It is later revealed that Akane's bracelet may have been flipped with the 6 actually being a 9. Santa's bracelet is then assumed to have a value of 0, another number which does not modify the digital root of a group to which it is added. In the developer Q&A, it is revealed that Santa's bracelet actually has the value of 9 while June's has the value of 0. This switch in values makes no difference however, since neither number modifies the digital root of the group of numbers to which they are added and that they always went through the same numbered doors. This is also hinted in the safe combination, because the numbers 3 and 6 are changed to 0 and 9.

It is also interesting to note that adding the numbers 1-9 together gives a result of 45; 4 + 5 = 9. Thus, it is possible for every player to enter every set of numbered doors if they all worked together:

- The first set: [4] and [5], add up to 9.
- The second set: [3], [7], and [8], add up to 18; 1 + 8 = 9.
- The third set: [1], [2], and [6], add up to 9.
- The final set: the two [9] doors in the chapel have a digital root of 9.

Door q in the incinerator is a special case during the Second Nonary Game because it was programmed to open with a digital root of 8.

## Trivia

- Another way to calculate the digtal root of any given number is to calculate its modulo 9, which is the remainder of the division by 9 of that number. If the resulting number is 0, the digital root of that number is [9], unless the number in question is 0, in which case the result is [0].
- The reason why modulo 9 resulting 0 gives a digital root of [9] is because in a division by 9, a remainder of 9 cannot exist, as the remainder can't be larger than the divisor. If a 9 appears in the remainder while dividing, the division will always have a remainder of 0.
- This is most likely the way that the calculator computes digital roots, as programatically speaking, this method is much more efficient than the one described in
*999*.