In advance, download the Arrowheads Puzzle template from the Resources tab.
Print the template on cardboard, or cut the puzzle pieces on a sheet of plywood.
Prepare and distribute one puzzle set (seven pieces) to each person/small group.
Each group aims to use the seven pieces of the puzzle to assemble five identical, simultaneous arrowhead shapes.
One solid arrowhead shape is provided as one of the seven pieces. The remaining four arrowheads are exactly the same size as this template.
When the puzzle is solved, everyone will be able to see all five arrowhead shapes at the same time.
Encourage your group to think synergistically.
Continue play until the puzzle is solved.
Video Transcript for Arrowheads Puzzle presented by Mark Collard
It’s possibly one of my favourites and it’s a new one. Now I have created it out of paper. Your object is to use these seven pieces to form five identically shaped arrowheads.
Now the actual arrowhead that I am looking to create the shape of is this one right here. So you can sort of get the sense of it being an actual arrowhead. So that is the one, that’s the gimme.
You have already got the first one it’s ready to go. Your object is to use the other six pieces and create four other arrowhead shapes. So that is your first one. Your object is to create a total of five. You need to do four more. Okay?
Great so now you got two.
(Can they connect or they have to be separate shapes, and do we need to have all four at the same time?)
All five, you need to have five identically shaped arrowheads.
(And have five separate?)
They are all quite separate, there’s no overlap, there’s no trick. You’ll end up with five shapes of arrowheads, identically shaped as each other. So there’ll be five of the same shape.
So you got all of the right pieces. Your object is to create five identically shaped arrowhead shapes. So you got four, you are still looking for one more.
I know exactly what you are struggling with, it is like I haven’t got any more pieces. You could do black, but it is so hard to see on the carpet to be honest. So it is still white, but it isn’t even about the colour, it’s about the shape.
(So can we use pieces again?)
You can, but remember it is all at once. When you are finished with it you’ll see five identically shaped arrowhead shapes.
I am not sure what you mean by separate shapes.
(So these are separate, but if we joined them up.)
See what you come with. Keep playing with that because right now you are one shape short, the one arrowhead short.
I can tell you that four of the arrows in the solution all point the same direction. That is one of the clues. Four of the five arrows all point in the same direction. It’ll help you if they are all white by the way too, there’s nothing to do with the colour.
So four arrows point the same direction, and how many shapes? Remember your objective was to find five identically shaped arrowheads. What have you got now? (Five) You got five yeah.
So what was one of the issues you had when you were first trying to solve the problem?
(Trying to make five out of that.)
Yeah right, and what was your first obstacle to that? Didn’t have enough pieces. So you are going “where are the pieces that I am missing? You can’t do it, I don’t have enough pieces.” Yet you were caught on when you heard me ask for the five identical shapes, you immediately thought they had to be physical, you thought they had to be the same colour.
How To Play Narrative
On its own, this puzzle can form part of your arrival activities, to keep people busy as they arrive, or as a full-blown small group initiative.
In advance, download the Arrowheads Puzzle template from the Resources tab. Print the template on cardboard, or if you’re feeling particularly industrious, cut the puzzle pieces on a sheet of plywood.
You’ll need one puzzle set (seven pieces) for each person or small group you wish to challenge. Small groups work best because the interaction between group members will provide an opportunity to build valuable team skills.
Having distributed the puzzle sets, issue this challenge – using the seven pieces, each group is to assemble five identical, simultaneous arrowhead shapes.
Explain that one solid arrowhead shape is provided as one of the seven pieces. The remaining four arrowheads are exactly the same size as this template.
Announce that when the puzzle is solved, everyone will be able to see all five arrowhead shapes at the same time. And that’s it.
Have a go yourself before you present this exercise to your group. Expect it to take longer than you think.
Try to resist, but if you must, you can download the solution from the Resources tab.
Practical Leadership Tips
Be careful with your presentation of this challenge, in particular, in regards your language. If your group understands from your delivery that they are to make five arrowheads with the seven pieces (which is not possible), you will lead them astray. Focus your briefing on producing five arrowhead shapes.
This puzzle is ideal for lessons which focus on how to solve problems with limited resources. Most people will quickly discover how to produce four arrowheads, but may struggle to find the fifth shape.
The solution also reflects the value of synergy (ie everyone working together towards the same goal,) where the sum of four arrowheads all pointing in the same direction equals five arrowhead shapes (not four.)
These arrowheads are a popular example of a tessellation, ie the repetition of a geometric shape with no overlaps and no gaps. So, if you keep adding more pieces, you’ll be able to produce an infinite number of arrowheads.
You could integrate Arrowheads Puzzle into a well-designed SEL program to inspire your group’s creativity and ability to embrace diverse ideas and different perspectives.
Specifically, this activity offers opportunities to explore and practice the following social & interpersonal skills:
Having A Growth Mindset
Controlling One’s Emotions
Identifying & Managing Stress
Demonstrating Self-Discipline & Self-Motivation
Demonstrating Empathy & Compassion
Recognising Strengths In Others
Seeking and/or Offering Support
Demonstrating Curiosity & Open-Mindedness
You can learn more about SEL and how it can support character education here.
Health & Wellness Programming
Emotional Intelligence & Resilience
The ability to cope with frustration and manage one’s emotions are two competencies that are worth reflecting on in advance and the conclusion of this fascinating Arrowheads Puzzle. Most people/groups struggle to see the ultimate solution in a short time frame, so it provides a wonderful opportunity to discuss coping mechanisms and understanding other perspectives.
In addition to the questions posed in the Reflection Tips tab, the following questions may be useful to help your group explore these issues:
What feelings did you experience during this puzzle?
At what point did you acknowledge that you were frustrated?
Did anything tip you over the edge?
Did anything help to manage your emotions at this time?
What did you think when the solution was presented to you? What did you say to yourself?
What did you need to let go of to see this solution?
This solution required a different perspective. Where else in your life would you benefit from a new perspective?
Trees: Adopt an environmental theme, and describe the shapes as trees. Cautioning your group that it may not, initially, see the forest for the trees, ask them to solve the puzzle.
Eight Arrowheads: Create two extra arrowhead shapes (complete or in two pieces) and invite your group to assemble eight arrowhead shapes in total.
Open the Virtual Adaptation tab to learn how to present this activity online.
In advance, share a digital copy of the Arrowheads puzzle template to each person and ask that they cut out the seven pieces of the puzzle. In small groups, invite the group to work together to create the solution. This online version will test the communication and patience skills of your group so facilitate as required.
Supply (or arrange) only one person with the seven puzzle pieces. If possible, focus the camera on the puzzle sitting on a table. Clearly, only one person can manipulate the puzzle and must be guided by the rest of their group members to move the pieces. An awesome task to focus on and develop communication, listening, planning and critical thinking skills.
For large groups, divide into smaller teams of 2 to 4 people and invite them to interact in their own breakout room to solve the problem. The first group to solve the puzzle and share a photograph of the solution wins (if that’s important.)
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Useful Framing Ideas
Knowing how to solve problems with limited resources is a really valuable life skill. Often the solution does not stare us in the face, but applying the collective knowledge and expertise of others, new possibilities start to emerge. This next exercise will be a wonderful example of this concept…
Synergy is often referred to as the ‘whole being greater than the sum of its parts.’ It’s a bit like saying 1 + 1 = 3. From a purely mathematical perspective, this solution may not seem plausible, but within the context of teams, it is totally possible. For example, let’s assume that each member of your group can produce 10 units of output. With 12 members in your team, you could expect to produce 120 units, right? However, if you were to work together synergistically, it is entirely possible to produce significantly more than 120 units with exactly the same resources. How is this possible? First, let’s explore this concept of synergy in a puzzle…
Reflection Tips & Strategies
Coupled with one or more reflection strategies, here are some sample questions you could use to process your group’s experience after playing this challenging team puzzle:
For most people, it takes a long time to solve this puzzle. Why?
What does this solution teach us about working as a team?
How might we apply what we have learned from this puzzle to our [ work, home, play ] life?
The inspiration for Arrowheads Puzzle, and many more team-based puzzles, was sourced in the following publications: