  We study the problem of treasure hunt in a Euclidean plane by a mobile agent
with the guidance of pebbles. The initial position of the agent and position of
the treasure are modeled as special points in the Euclidean plane. The treasure
is situated at a distance at most $D>0$ from the initial position of the agent.
The agent has a perfect compass, but an adversary controls the speed of the
agent. Hence, the agent can not measure how much distance it traveled for a
given time. The agent can find the treasure only when it reaches the exact
position of the treasure. The cost of the treasure hunt is defined as the total
distance traveled by the agent before it finds the treasure. The agent has no
prior knowledge of the position of the treasure or the value of $D$. An Oracle,
which knows the treasure's position and the agent's initial location, places
some pebbles to guide the agent towards the treasure. Once decided to move
along some specified angular direction, the agent can decide to change its
direction only when it encounters a pebble or a special point.
  We ask the following central question in this paper:
  ``For given $k \ge 0$, What is cheapest treasure hunt algorithm if at most
$k$ pebbles are placed by the Oracle?"
  We show that for $k=1$, there does not exist any treasure hunt algorithm that
finds the treasure with finite cost. We show the existence of an algorithm with
cost $O(D)$ for $k=2$. For $k>8$ we have designed an algorithm that uses $k$
many pebbles to find the treasure with cost $O(k^{2}) + D(\sin\theta' +
\cos\theta')$, where $\theta'=\frac{\pi}{2^{k-8}}$. The second result shows the
existence of an algorithm with cost arbitrarily close to $D$ for sufficiently
large values of $D$.
