T Puzzle: UWT Four-Piece Version

Choose this exercise

Purpose: Arrange four geometric pieces into an exact capital T silhouette without gaps or overlapping edges.

Use it when: Use as a focused team warmup or transitional exercise to examine how groups test hypotheses, challenge unstated assumptions, and handle stuck states.

Skip it when: Skip when the session lacks tables or flat assembly surfaces, or when the group needs conceptual discussion rather than a concrete mechanical puzzle.

Group arrangement: Pairs or trios

Timing: Based on the 5 to 15 minute band in observed records; 15 minutes provides ample time for assembly attempts, solution reveal, and debrief.

Materials and tools

• One envelope containing the 4 cutout pieces per group, pre-cut from heavy paper or cardstock
• One printed target sheet showing the full T silhouette per group
• One printed facilitator solution sheet kept private by the facilitator
• Scissors for setup preparation
• Scratch paper and pen per group for drafting ideas

Before participants arrive

1. Print cutout sheets on cardstock at 100 percent scale.
2. Using scissors, carefully cut out the four pieces for each set.
3. Test-fit every set against the target sheet to ensure accurate cut edges.
4. Place each four-piece set into an opaque envelope.
5. Print one target sheet per team and keep the solution sheet hidden.

Say this to open

Your table has four geometric pieces and an outline of a capital letter T. Working together, arrange all four pieces to fill the outline completely. Pieces must lay flat with no overlaps, gaps, or folds. You may rotate pieces or flip them over. You have seven minutes to solve it.

How to run it

1. Introduce challenge and distribute sets 2 minutes

   Welcome the room and explain the objective using the opening script. Distribute one envelope of four pieces and one target silhouette sheet to each pair or trio. Confirm everyone understands that pieces must lay flat without overlapping or bending.

2. Assemble the T 7 minutes

   Start the timer. Groups manipulate the four pieces flat on the table, testing orientations against the target silhouette. Move between groups to observe interactions and verify pieces remain flat. Do not give placement hints. If a team solves it early, instruct them to scramble the pieces and reproduce the solution once more.

3. Display solution and compare 3 minutes

   Call time on testing. If any group succeeded, invite them to let neighbors view their layout. For groups still working, display the facilitator solution diagram or guide them to place Piece 4 across the top seam. Give everyone 90 seconds to match the finished layout.

4. Debrief problem-solving process 3 minutes

   Run a brief whole-room debrief using the prompt questions. Collect up to three observations about common layout assumptions, communication, and how teams decided to abandon an approach that stalled.

Debrief questions

• Where did your team assume the straight edges or diagonal seams had to go?
• What signal told your group to scrap a layout rather than keep nudging the same pieces?
• How did your group manage turns or agree on which layout to test next?

Finished output: Four polygon pieces arranged to fill the target capital T outline without gaps or overlaps, or an analyzed record of attempted layouts.

Remote

Distribute a slide or virtual whiteboard file to each breakout pair with the four polygon vector shapes placed beside the target outline. Enable rotation and free movement. Pairs work in breakout rooms for 7 minutes, then return to the main room.

Hybrid

Remote participants manipulate digital polygon shapes on a shared vector canvas while in-person pairs assemble paper cutouts. In-person tables point a webcam at their workspace or upload a final photo so both cohorts compare layouts.

Access and participation choices

• Participants who prefer not to manipulate small pieces can direct placement verbally, track trial configurations, or observe.
• Any participant may decline hands-on manipulation or pass during debrief questions without explanation.

If the session gets stuck

Participants believe their cut pieces are missing an edge or misprinted.

Remind them that all four pieces form the exact 3x3 T silhouette when correctly angled, and suggest testing diagonals that cross between the stem and the bar.

One team member dominates the physical cutouts while others disengage.

Pause the group and suggest taking single-piece placement turns, or have the non-handling partner dictate moves while the other places pieces.

Terms used here

• Dissection: The act of dividing a geometric shape into smaller polygon pieces that reassemble into target shapes.

T-Puzzle Cutout Sheet

Cut along all solid outer lines to create four distinct puzzle pieces. Do not fold pieces.

Print on cardstock at 100 percent scale without fit-to-page margins.

T-Puzzle Target Silhouette

Assemble all four pieces to match this capital T silhouette. The finished shape must match these exact outer dimensions without overlapping pieces or empty gaps.

Facilitator Solution Key and Coordinate Data

FOR FACILITATOR USE ONLY. Keep hidden from participants until the reveal.

Coordinate specification (x right, y down, 3x3 total bounding box; top bar width 3, height 1; stem width 1, height 2):Piece 1 (pentagon): (0,0), (0,1), (1,1), (1,1.25), (2,1.5)Piece 2 (trapezoid): (1,1.25), (2,1.5), (2,3), (1,3)Piece 3 (triangle): (3,0), (3,1), (2,1)Piece 4 (quadrilateral): (0,0), (3,0), (2,1), (2,1.5)