Task 96
Task 96: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In the five-sided star shown, the letters $A$, $B$, $C$, $D$, and $E$ are replaced by the numbers 3, 5, 6, 7, and 9, although not necessarily in this order. The sums of the numbers at the ends of the line…
The task
In the five-sided star shown, the letters $A$, $B$, $C$, $D$, and $E$ are replaced by the numbers 3, 5, 6, 7, and 9, although not necessarily in this order. The sums of the numbers at the ends of the line segments $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, and $\overline{EA}$ form an arithmetic sequence, although not necessarily in this order. What is the middle term of the arithmetic sequence? [asy] pair A,B,C,D,E; A=(0,10); B=(5.9,-8.1); C=(-9.5,3.1); D=(9.5,3.1); E=(-5.9,-8.1); draw(A--B--C--D--E--cycle,linewidth(0.7)); label("$A$",A,N); label("$B$",B,SE); label("$C$",C,NW); label("$D$",D,NE); label("$E$",E,SW); [/asy]