Question 1127640: Given the set {1,2,3,6,11,20,37,68,}, which integers between 60 and 100 cannot be written as a number from the set on it's own, or as the sum of two, three or four numbers from this given set?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
There is no magic formula for answering a question like this. You simply need to look at each number from 60 to 100 and see if you can make each one with the given ground rules.
Start with 60; and always use the largest numbers you can. Here's the start:
Until you get to 68, the largest numbers you can use are 37 and 20. Since 37+20=57, you can find...
60 = 37+20+3
61 = 37+20+3+1 (1 more than 60; add the 1}
62 = 37+30+3+2 (1 more than 61; replace the 1 with 2)
63 = 37+30+6 (1 more than 62; replace the 3+2 with 6)
64 = ....
You need to see if you can make all the other numbers up through 67 with the given ground rules.
Then when you get to 68 it gets a bit easier for a while.
68 = 68
69 = 68+1
70 = 68+2
71 = ...
You can see that each time you get to a number that can be made with either one or two of the given numbers, you will be able to get the next several using the 1, 2, 3, and 6.
So you will be able to get the next several numbers after 68+11=79, and the next several after 68+20 = 88.
I leave it to you to do the rest of the work.
There are only two numbers from 60 to 100 that you can NOT make with the given ground rules; I'll let you find them.
|
|
|
