Treasure Hunt
1 out of 3
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Problem
Can you find the hidden treasure?
Watch the video for an introduction or scroll down to have a go using the interactivity.
The treasure has been hidden somewhere where the grid lines intersect (cross).
Input coordinates to help find the treasure with the fewest guesses. The interactivity gives you the shortest distance you'd have to travel (along the grid lines) to reach the treasure.
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses? How do you know that your strategy will always work?
Click on the purple cog when you are ready to tackle more challenging versions.
Getting Started
Try to decide which places are good for first guesses.
Once you've got feedback on your first guess identify all the possible places where the treasure could be. What pattern does this make?
Have another guess. Use the feedback to identify all the possible places where the treasure could be.
Now use the feedback from both guesses to find some overlapping points.
Continue in the same way...
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem offers students a chance to consolidate their understanding of coordinates whilst challenging them to think strategically and work logically.
Possible approach
You may find it useful to print off these grids if your students do not have access to the interactivity.
This problem featured in an NRICH Primary webinar in November 2021, and in an NRICH Primary and Secondary webinar in September 2022.
Demonstrate the Level 1 problem to the class, either using the interactivity or with a grid drawn on the board.
Give students about 10 minutes to work on the problem, either at computers, or on paper in pairs (taking it in turns to choose where the treasure is and give the distances). Pairs can keep score of the number of guesses each student required to find the treasure - the one with the lowest score wins.
Ask the class to share efficient strategies/useful ideas. Encourage the students to consider all the points that satisfy each condition, and to look at the shape of this locus. Re-emphasise that the problem is to develop a strategy to find the treasure with the minimum number of guesses (at Levels 1 and 2, with the appropriate strategy, it is always possible to find the treasure in fewer than four guesses).
Return to the computers/pairs to work on the suggested strategies. Provide squared paper for rough jottings.
If students are familiar with coordinates in four quadrants, the Level 2 game can be an excellent context for practising these. (The level can be changed by clicking on the purple cog in the top right of the interactivity.) Encourage students to do their work on paper.
Key questions
Which points satisfy the conditions given so far?
How can you narrow down the possibilities?
Possible support
Encourage students to draw the grid on squared paper, and colour code points that are possible; looking at the result of each new piece of information.
Possible extension
The Level 3 game provides an interesting challenge: the searching area is restricted to the pink region, although the treasure may be anywhere on the grid. Users are allowed one 'final answer' guess outside the pink region to locate the treasure.
The Level 4 game provides a challenging context in which to think about 3-dimensional coordinates and it can be explored in 3D Treasure Hunt.
Again, the challenge is to develop a strategy to find the treasure with the minimum number of guesses (at Levels 3 and 4, with the appropriate strategy, it is always possible to find the treasure in fewer than five guesses).
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