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Patterns Generate Number

Patterns Generate Number practice with visual examples, common slips, and next-step routes.

Surface

This skill appears in Recurrence or cycle target entry, Digit-sum stopping step count, Equalizing-growth first-day count, Repeating-jump state pair, Visual growing-pattern count extension.

Task formats

Digit-sum stopping step count

Digit-sum stopping step count asks the player to apply the decimal digit-sum transition until the first one-digit state, then choose the exact number of transitions taken.

ActionApply the decimal digit-sum transition until the first one-digit state, then choose the exact number of transitions taken.
CheckComplete the digit-sum stopping step count action.
UseSupport / Core / Transfer
ShowsCheck only
PresentationCompact / Standard / Extended

Practice focus

Balanced growth

Equalizing-growth first-day count

Equalizing-growth first-day count asks the player to use an exact day-indexed arithmetic rule and a fixed threshold to choose the earliest positive integer day on which the strict target relation holds.

ActionUse an exact day-indexed arithmetic rule and a fixed threshold to choose the earliest positive integer day on which the strict target relation holds.
CheckComplete the equalizing-growth first-day count action.
UseSupport / Core / Transfer
ShowsCheck only
PresentationCompact / Standard / Extended

Practice focus

Balanced growth

Recurrence or cycle target entry

Recurrence or cycle target entry asks the player to infer the recurrence or cycle from exact state rules and enter the requested term number or cycle-state index.

ActionInfer the recurrence or cycle from exact state rules and enter the requested term number or cycle-state index.
CheckEnter or choose the number that matches the task.
UseSupport / Core / Transfer
ShowsCheck only
PresentationCompact / Standard / Extended

Practice focus

Balanced growth

Repeating-jump state pair

Repeating-jump state pair asks the player to apply the repeating jump rule to the target step and submit the ordered pair describing the resulting jump state.

ActionApply the repeating jump rule to the target step and submit the ordered pair describing the resulting jump state.
CheckComplete the repeating-jump state pair action.
UseSupport / Core / Transfer
ShowsCheck only
PresentationCompact / Standard / Extended

Practice focus

Balanced growth

Visual growing-pattern count extension

Visual growing-pattern count extension asks the player to extend the coded growing pattern to a specified target stage and enter the exact number of the declared unique elements.

ActionExtend the coded growing pattern to a specified target stage and enter the exact number of the declared unique elements.
CheckComplete the visual growing-pattern count extension action.
UseSupport / Core / Transfer
ShowsCheck only
PresentationCompact / Standard / Extended

Practice focus

Balanced growth

Selection

Fresh independent work can move toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.

Help

Hints keep attention on the visible structure; reveals show the path without counting as independent evidence.

Presentation

Presentation can reduce reading and interaction load without changing the selected skill. Practice focus can bias compatible work without breaking prerequisites or story fit.

Story fit

  • Contexts that preserve the canonical mathematical action without changing the response or answer rule.