Maple can solve the easiest two problems of the Putnam Mathematical Competition 2018. link
Problem A1
Find all ordered pairs (a,b) of positive integers for which 1/a + 1/b = 3/2018
> 
eq:= 1/a + 1/b = 3/2018;


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(2) 
> 
# Unfortunalely Maple fails to find all the solutions; eq must be simplified first!


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> 
remove(u >(eval(a,u)<=0 or eval(b,u)<=0),[s]);


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Problem B1
Consider the set of vectors P = { < a, b> : 0 ≤ a ≤ 2, 0 ≤ b ≤ 100, a, b in Z}.
Find all v in P such that the set P \ {v} can be partitioned into two sets of equal size and equal sum.
> 
n:=100:
P:= [seq(seq([a,b],a=0..2), b=0..n)]:

> 
k:=nops(P): s:=add(P):
numsols:=0:

> 
for i to k do
v:=P[i]; sv:=sv;
if irem(sv[1],2)=1 or irem(sv[2],2)=1 then next fi;
cond:=simplify(add( x[j]*~P[j],j=1..k))sv/2;
try
sol:=[];
sol:=Optimization:Minimize
(0, {x[i]=0, (cond=~0)[], add(x[i],i=1..k)=(k1)/2 }, assume=binary);
catch:
end try:
if sol<>[] then numsols:=numsols+1;
print(v='P'[i], select(j > (eval(x[j],sol[2])=1), {seq(1..k)})) fi;
od:
'numsols'=numsols;


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