B1. Anouk, Bart, Celine, and Daan participated in a math competition. Each of their scores is a positive integer. Bart and Daan together scored exactly as many points as Anouk and Celine together. Anouk and Bart together scored more points than Celine and Daan together. Daan scored more points on his own than Bart and Celine together.

Write the names of the four students in order from highest to lowest score.
1. A, D, B, C Let the scores of Anouk, Bart, Celine, and Daan be $a, b, c$, and $d$ respectively. The problem tells us that

$$
b+d=a+c, \quad a+b>c+d \quad \text { and } \quad d>b+c \text {. }
$$

By adding $a$ to both sides of the left equation, we get $a+b+d=2a+c$. By adding $d$ to both sides of the middle inequality, we get $a+b+d>c+2d$. When we combine these, we see that $2a+c>c+2d$. This implies that $a>d$.

We now know that $a>d>b+c$, so Anouk has the highest score and Daan has the second-highest score. From the equation $b+d=a+c$ and $a>d$, it also follows that $b+d>c+d$ and thus $b>c$. Therefore, the order of the participants is: Anouk, Daan, Bart, Celine.