Question 24
For real numbers $a,b,c,d,e$, it is given that $$a=|b|-|b-1|,\qquad b=|c|-|c-1|,$$ $$c=|d|-|d-1|,\qquad d=|e|-|e-1|.$$ If $a=\frac12$ and $e=\frac{x}{y}$, where $\operatorname{HCF}(x,y)=1$, find $x+y$. Take $x,y$ to be positive integers, so that the fraction is in its usual reduced form.
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).