ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

Changes to the Procedure - contributed by Shane Baggs

 h. Now attach the second group (three numerals) of the cube number, to the residue of the first group. Add 1 to the "root" number and add the sum of the "root" number to the square number. Then add 0 to the "root" number and add 11. **Add 00 to the "square" number, then add the "root" number to the "square" number. For example: If the total "root" number is 61 and the square number is 12, the new square number will be 1261. j. If, after attaching a new group of the "cube" number, the "square" number is still too large, attach an additional group but instead of adding 0 to the "root" number, followed by the addition of 11, in this case add 00 followed by the addition of 101. ***Then instead of adding 00 to the "square" number, we add 0000. The "root" number is then added to the "square" number.

Reason for the Changes - contributed by Nanami Kamimura

Crook used two-digit numbers in his examples in the "root" and "square" numbers. However, the "root" number does not always have two digits. Sometimes, it has one or three digits. This is also true with the "square" number. Sometimes it has one digit; other times it has three.

Following Crook's instructions word by word may cause confusion and/or will not work. For example if the "root" number has three digits and the "square" number has only two; following Crook's instructions will result in a five-digit number that is potentially larger than the remainder of the first group of the "cube" number and the current second group of the same "cube" number combined.

Using Crooks original wording, here are two examples where problems can occur

Cube root of 110,592 = 48
Cube root of 262,144 = 64

Thanks to both Nanami and Shane for their contributions to this technique.

Shane Baggs & Nanami Kamimura
September, 2007