There are some flowers along the corridor arranged in the following order:  $5$ purple, $3$ red, $2$ yellow, $2$ pink, $3$ red, $2$ yellow, $2$ pink $\cdots$  If there are $100$ flowers altogether, how many red flowers are there altogether? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems
$$3+2+2=7$$;  $100-5=95$  $95\div7=13R4$;  $$13$$$\times$$$3$$+$$3$$=$$42$$. 