p1. Find an integer that has the following properties:
a) Every two adjacent digits in the number are prime.
b) All prime numbers referred to in item (a) above are different.


p2. Determine all integers up to $\sqrt{50+\sqrt{n}}+\sqrt{50-\sqrt{n}}$


p3. The following figure shows the path to form a series of letters and numbers “OSN2015”. Determine as many different paths as possible to form the series of letters and numbers by following the arrows.
[img]https://cdn.artofproblemsolving.com/attachments/6/b/490a751457871184a506c2966f8355f20cebbd.png[/img]


p4. Given an acute triangle $ABC$ with $L$ as the circumcircle. From point $A$, a perpendicular line is drawn on the line segment $BC$ so that it intersects the circle $L$ at point $X$. In a similar way, a perpendicular line is made from point $B$ and point $C$ so that it intersects the circle $L$, at point $Y$ and point $Z$, respectively. Is arc length $AY$ = arc length $AZ$ ?


p5. The students of class VII.3 were divided into five groups: $A, B, C, D$ and $E$. Each group conducted five science experiments for five weeks. Each week each group performs an experiment that is different from the experiments conducted by other groups. Determine at least two possible trial schedules in week five, based on the following information:
$\bullet$ In the first week, group$ D$ did experiment $4$.
$\bullet$ In the second week, group $C$ did the experiment $5$.
$\bullet$ In the third week, group $E$ did the experiment $5$.
$\bullet$ In the fourth week, group $A$ did experiment $4$ and group $D$ did experiment $2$.
1. **Week 1**: \( D \) - 4
2. **Week 2**: \( C \) - 5
3. **Week 3**: \( E \) - 5
4. **Week 4**: \( A \) - 4, \( D \) - 2
5. **Week 5 possibilities**:
    - Schedule 1: \( A \) - 1, \( B \) - 2, \( C \) - 3, \( D \) - 5, \( E \) - 4
    - Schedule 2: \( A \) - 3, \( B \) - 1, \( C \) - 2, \( D \) - 5, \( E \) - 4

The final answer is $\boxed{\text{Schedule 1: } A - 1, B - 2, C - 3, D - 5, E - 4 \text{ and Schedule 2: } A - 3, B - 1, C - 2, D - 5, E - 4}$.