Permutation Sum Problem

I have a problem, it my require a formula and it may require some programming logic but I feel like there is a simple way to solve this problem but I just cant see it.

I have a part that changes length between 8 and 60 inches [L] . I have 5 other parts, each with a discrete length between 5 and 7 inches i.e X1=5, X2=5.5, X3=6, X4=6.5, X5=7. I need to find some way of filling up the arbitrary length[L] such that with any permutation of discrete X values I can sum them up and when subtracted from L the remainder is less than 1.

Given an arbitrary length [L] and a DISCRETE quantity of lengths between N=5 and B=7 [N<X1,X2,X3,X4,X5<B]. Find a formula

I have a problem, it my require a formula and it may require some programming logic but I feel like there is a simple formula to solve this problem but I just cant see it.

I have a part that changes length between 8 and 60 inches [L] . I have 5 other parts, each with a discrete length between 5 and 7 inches i.e X1=5, X2=5.5, X3=6, X4=6.5, X5=7. I need to find some way of filling up the arbitrary length[L] such that with any permutation of discrete X values I can sum them up and when subtracted from L the remainder is less than 1.

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Given an arbitrary length [L] and a DISCRETE quantity of lengths between N=5 and B=7 [N<X1,X2,X3,X4,X5<B]. Find a formula that will g

I am running a whole bunch of small AC motors off of a 120v-24v 250VAC transformer. I am using a programmable relay switch to turn this circuit on and off every 30 seconds for weeks at a time. Do I have to worry about any back emf or inductance in the transformer depending on whether I place the relay before the transformer or after?

Edit: Thanks for the answers. I will be switching from the load side.