Problem 20 worked answer

The Defect’s 100th Orb

Designed for Grade 3 · Uses Early Grade 3 math · About 3–8 minutes

Earn one jewelIndicoliteLevel 3

At a glance

  • Part 1: The Orbs Evoked are Lightning, Frost, Dark. The slots return to Dark, Frost, Lightning.
  • Part 2: The 100th channel Evokes Lightning.

1. One complete set of channels

The starting slots are Dark, Frost, Lightning, from left to right.

  • Channel Lightning: the starting Lightning Orb is Evoked, leaving Lightning, Dark, Frost.
  • Channel Frost: the starting Frost Orb is Evoked, leaving Frost, Lightning, Dark.
  • Channel Dark: the starting Dark Orb is Evoked, leaving Dark, Frost, Lightning.

The Orbs are Evoked in the order Lightning, Frost, Dark. After the three channels, the slots are back in their starting order: Dark, Frost, Lightning.

2. The 100th channel

Every three channels restore the starting slots, so the Evoked-Orb pattern repeats:

Lightning, Frost, Dark, Lightning, Frost, Dark, …

Since , the 100th channel begins a new repeat. The Orb Evoked on that channel is Lightning.

The key insight is that there is no need to track 100 separate rows. Once the same three-slot state returns, all later steps repeat in groups of three.

Check

The 99th channel is the last channel in the 33rd complete group, so the 100th channel must match the first channel in the pattern. That first channel Evokes Lightning.

Technical fit and rating

MJ 3.1 · C3 · W1 Stretch challenge · Light workload

Patterns and algebra

How the rating works →

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