About Digital Roots

The digital root file.

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.


  • 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.

Numbers 0/9

In the Nonary Game, the numbers 0 and 9 are extremely valuable and versatile numbers, as they will not change the digital root of the number(s) they are added to. This means that the bearer of a bracelet with the (true value) of 0 or 9 can more easily control their fate than the other players, as they can join any team whose digital root is 9 to enter Door 9, even teams of two.

The only character who has a bracelet that displays the number 9 is Teruaki Kubota.

Snake theorizes that Akane's bracelet has 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 questions 9 and 46 of the 999 developer Q&A, it is revealed that both Santa's and Akane's true values are 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.

There is a theory that Aoi's bracelet is 9, but this has never been officially proven. Given the combination that opens the safe/coffin (14383421) and multiplying it by 9 is 129450789. This could reveal the actual values of all the bracelets, as it is a sequence of numbers from 1 to 9, where 3 (Santa's number) and 6 (Akane's number) are replaced by other numbers, one could theorize his true value is 9. However, this has never been confirmed. Aoi's bracelet number could be seen as being both 0 and 9 at the same time like his sister's.

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 does not use digital roots.


  • Another way to calculate the digital 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.