Laura is in charge of lighting the Rock Palace for an upcoming concert. Each light fixture supplies exactly 1,000 watts of power to light the bulbs in the fixture. Laura can use any combination of 150-watt, 100-watt, 75-watt, or 60-watt bulbs, but the total number of watts must be 1,000. How many different combinations of bulbs can you find that Laura could use in a light fixture?

I need to list all the combos and the total are 28, please help.

How would you start to figure this problem out?

This is tedious work, but if you're systematic, you can get them all :)

Start taking as many 150-watt bulb as possible. Maximum, for example is 6, giving you:

6 (150-watt) + 1 (100-watt) = 900 W + 100 W = 1000 W

Is there a way to express the 100-watt bulb with other smaller bulbs? No, hence, reduce the 150-watt bulb by one.

5 (150-watt) + ? = 1000 W

5 such bulbs give 750 W, you need 250 W. Is that possible to get from other bulbs? Yes, using 1 (100-watt) and 2 (75-watt). You continue as such decreasing the 150-watt bulbs, until you reach 0 of them. Then, you pick the maximum number of 100-watt bulb, decrease that number each time after getting all the combinations, and no more looking into the 150-watt bulb (since you would have got all combinations of them now). Okay, so the first two are:

6 (150-watt) + 1 (100-watt)
5 (150-watt) + 1 (100-watt) + 2 (75-watt)

Can you get the other 26?

PS: I haven't counted them all, but if there are any errors in the (or your) answer, we'll see as soon as you submitted your work :)

(5*2) +(21-18)=

(5*2) +(21-18)=

(5*2) + (21-19)=