Would someone be kind enough to write rsolve procedures (or code) to evaluate these two sums

the answers are 3 and 7/4

regarding optimization, we know about inputs like "assume=integer". I want to instruct Maple that the variables in my problem are required to be unique.

eg I have three variables a,b,c that could take values 1,3 or 4 (but not 1,1,2 or 2,3,3 ....etc).

With DirectSearch I could always add the constraint {a<>b, b<>c, a<>c}, but it gets complicated if you have more than 3 variables. Additionally Maples Optimization package...

next_fib.mw

I want to find the next fib number in the sequence given an input number.

I know there are previous posts using a recurance formula...i don't want to do that.

I want my code to work like the nextprime command. but i have problems..

If the number i/p is not a fib no. .....error.  it needs to find the next actual fib no.

there is also the problem that because the...

silver_coin_braintea.mw

Experts. This is something like the subset sum problem with a twist.

Jane has some Australian silver coins in her pocket. When buying an apple, she
realises she has more than $1 in silver coins, but can’t make exactly $1 with
her coins. How is this possible? (Silver Australian coins come in 5c, 10c, 20c,
and 50c.)

answer: obviously, you can't...

i need some help writing code to find the arithmetic sequences of primes. eg the arithmetic sequence of primes 7,37,67,97,127,157 differ by 30 each time, but runs out after 6 primes (187 is not prime). Is there a sequence of 7 primes? (i'm sure there is).. i want to investigate.......