Many of you have attempted to solve the
problem for levels 1 and 2. The same method can be applied to both
levels and the robber can always be located in 3 guesses. We
received very detailed answers from Eleanor (Radstock Primary) and
Liam (Thomas Deacon Academy). Although Eleanor didn't get the exact
right answer, she had the right ideas about how to approach the
problem. Here is her example for level 1:
First, I chose the middle of the grid, as I decided it would be the
best random place to start. The co-ordinates were (6, 6). I was 5
away from the robber.
I then looked at which spaces it could possibly be. I decided on 5
spaces to the right, the co-ordinates (11, 6), and that was 2
spaces away. I then looked at all the spaces that were 5 away from
(6, 6) and 2 away from (11, 6).
I tried the co-ordinates (10, 7) as they were 2 away from (11, 6)
and 5 away from (6,6). I was still 2 spaces away. I then chose the
co-ordinates (10, 5) as they matched all the other clues and I was
right, I found the robber in 4 guesses.
My strategy was to look at all the places it could be and then pick
the most likely one. I tried it like that again and it worked in 4
Her example can be illustrated
However, she could have saved 1 guess by
starting at other points. Mike and Andy from Old Earth School got
closer to the right answers by choosing their starting point at the
bottom left-hand corner:
Level 1: pick the co-ordinate (0,0) as your first point. The
possible places are the co-ordinates that add up to the number
indicating how far you are away from the robber. All of them are in
a straight line.
For Example if the distance is 6 the robber could be at (0,6),
(1,5), (2,4), (3,3), (4,2), (5,1), (6,0).
If you now choose a point at the end of the line, it will tell
you how far you are away and help you navigate to a specific point
on the straight line, where the robber is.
Their explanation can be illustrated by the
Level 2: We found if we choose (0,0) as our first point, we might
get 2 lines to choose from for our second guess. So we chose the
bottom left hand corner to start with and we got only one line
again. It made us realise that we only choose (0,0) as a starting
point if it is at the corner of the graph.
Elijah, working at home, sent in the following
First I started by choosing (6,6) as my first guess. After a while
I realised that this gave me too many possible hiding places and
thought that if I started in a corner of the grid then I wouldn't
have so many.
First guess: (0,0)
Second guess: (12,0)
Each guess gives a diagonal line of possible hiding places, and
only one point is on both lines. This is the robber's hiding place
and so you only need 3 guesses to find him.
I used the same strategy. My first two guesses were the bottom two
corners of the grid, whatever those coordinates are.
LEVEL 3 With the pink zone, I had to use four guesses.
First guess: use the point which is in the middle of one end of the
pink zone. Then the possible hiding places make either a straight
line or a triangle.
Second guess: pick a point which is somewhere near the line (just
makes the numbers smaller and easier), on one edge of the pink
zone. This narrows down the choices from the first guess, and gives
Third guess: pick any point in the pink zone which would give you
two different distances to the two possible hiding places.
Fourth guess is the robber's hiding place, depending on answer to
LEVEL 4 First of all we had to work out how to think about this
problem. My mum worked it out. She tried drawing 3d pictures on
squared paper, and then on isometric paper, but they were both too
confusing. Then she remembered games of 3d chess and 3d noughts and
crosses and so she drew ten 9x9 grids, and labelled them z=0 up to
First guess: (0, 0, 0) I marked all the possible points that were
the right distance away - these came out as diagonal lines on the
grids. (Don't have to be on each of the ten grids.)
Second guess: (9, 0, 0) I used this one because it was the same as
the second guess from Level 1. Marked all the possible points
again, which gave diagonal lines going the other way, so where they
crossed gave some possible hiding places.
Third guess: we took a few goes to work out what was the best point
to use for our third guess. We wanted to use another corner of the
cube, but our first couple of tries gave us sets of points that we
had already got from our first two guesses. We decided on (0, 0, 9)
Marked the possible points again, and that gave only one possible
Fourth guess: robber's hiding place.
Elijah and his mum sent this photo of
Well done - you obviously worked hard on this