On the Subject of Trying to Un-Ancient-Obvious-ify Partitions

Help.

This module displays a rectangular grid of regions. Highlighting a pixel will reveal the index and value of the group it belongs to (displayed as INDEX/TOTAL:VALUE). In order to solve the module, you must group the current groups until there is just one left. Initially there are 10 groups.

In order to obtain the grouping, repeat the following process until all groups are regrouped:

1. Take the sum of all group values, this will be called Sgv
2. Obtain i = (Sgv % Gc) + 1, where Gc is the amount of groups currently shown on the module
3. Take the value of the i^th group on the module (the group that shows i when highlighted). This value will be called Gv
4. Obtain Ngs = (Gv ⨬ Us) + 1, where Us is the amount of ungrouped squares (10 for the first iteration of stage 1).
   ⨬ is a custom operator, named “reductive-modulo”. It behaves as follows for a ⨬ b
• If a < b, return a.
• Otherwise, do the following in order: a = a - b, b = b - 1
• Try step 1 again with your new a and b
• If b = 0 before a < b, return 0.
5. Disregard the i^th current group for all steps, except for step 4. This means Gc = Gc - 1, Us = Us - Ngs, and Sgv = Sgv - Gv. Ngs is the size of one of the new groups.

To submit your groups, select an amount of regions. Press a region, highlight until there are as many groups selected as required for a group, then press one of the selected regions. These regions will no longer be selectable for further groups and they will not reveal their colour again until a strike incurs or the module advances.

The shapes of these groups or the order of entering them do not matter. Groups may even be disconnected