Nim Relay: Don't Take the Last Cone

A relay strategy game based on the classic game of Nim: two teams take turns running out to remove 1, 2 or 3 disc cones from a pile, and whoever takes the last one loses. It combines running, math and team decisions.

How to play

1. Make 6 teams of 4 and pair them up in 3 lanes. In each lane, put a pile of 21 disc cones in the middle and each team's line 12 yards away, marked with cones (2 min).
2. Team A goes first: its runner goes to the pile, takes 1, 2 or 3 discs, comes back and high-fives the next runner. Only then does Team B's runner go (2 min to explain).
3. Teams keep alternating until one takes the last disc and loses the round; the other team scores a point.
4. Between rounds, take a 30-second huddle to work out how many discs to leave; the losing team starts the next round.
5. Play rounds for 7 minutes, then switch opponents and play another 7 minutes.
6. Wrap-up: teams that discovered the winning strategy (leave a multiple of 4) explain it to the class.

Rules

• Each runner takes 1 to 3 discs; never zero and never more than three.
• No one leaves until the opposing runner has crossed their line.
• Teammates may advise the runner, but the runner makes the final call.
• Safety: each team runs on its own side of the pile to avoid collisions.

Variations

Adaptations

• Limited mobility: the student is the strategist who decides the amount, or covers a shorter distance.
• Visual impairment: line the discs up along a rope so they can be counted by touch.
• Lower fitness: the student may power-walk the relay with no penalty.

Learning goals

• Apply logical reasoning to tactical decisions while fatigued.
• Reach team decisions quickly.
• Accept losing and analyze it to improve.

Equipment for a class of 25

• disc cones: 63
• cones: 12

Teacher tip

Let students discover the strategy themselves; if nobody sees it after three rounds, ask what happens when 4 discs are left. Rotate opponents so the same team doesn't always win.

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