Well done to Trevor from Riccarton High School, and also to Erin, for dealing with each of the three coordinates one at a time.

Keeping two coordinates fixed, while changing the third coordinate and noticing whether the distance to the target metagiff increased or decreased, then stopping when no further decrease is possible, certainly locates the target in the end.

Once we have a method that works the next challenge is to locate the target using the minimum number of guesses.

Michael used algebra to do this.

I needed to draw a diagram to follow his algebra, here is the diagram I drew.

(Remember wherever possible to include a diagram to help readers follow your working)

If the metagiff is at point $M$ with coordinates $a$, $b$, and $c$ in the $x$, $y$, and $z$ directions respectively then the difference between the result for $(0,0,0)$ and the result for $(0,0,9)$ will depend only on $c$ because $a$ and $b$ are included in the total distance for both results .

For example if $c$ was $7$, $R(0,0,0)$ would be $a+b+7$ and $R(0,0,9)$ would be $a+b+(9-7)$, or rather $a+b+2$;

In general $c$ is half of ($R(0,0,0) - R(0,0,9) + 9$)

The same logic can be used to find $a$ and $b$:

$a$ is half of $(R(0,0,0) - R(9,0,0) + 9)$

$b$ is half of $(R(0,0,0) - R(0,9,0) + 9)$

So the four results $R(0,0,0)$, $R(9,0,0)$, $R(0,9,0)$ and $R(0,0,9)$ are enough to locate the target.

Do you think you could find the
metagiff in less than 4 moves?

If so, how, and will it work in all
cases?