# Scrap puzzle to count how many

There are 250 scraps. For each 11 removed, one extra can be obtained. How much maximum is possible, if one cut by one unit?

I have read this somewhere, and one guy gave the answer as 25, but I can't understand why. Can anyone please explain?

• so what is the question? – Novarg Mar 16 '15 at 19:33
• I red the same exact riddle with cigarette butts and a hobo. He collected the butts and for each 7 butts he could create a cigarette. Assuming he collects 50 butts in a day, how many cigarettes he could create? – Narmer Mar 17 '15 at 8:57

This can be proven using math (the hard way):

250 - 11 = 239, 239 + 1 = 240
240 - 11 = 229, 229 + 1 = 230
230 - 11 = 219, 219 + 1 = 220
220 - 11 = 209, 209 + 1 = 210
210 - 11 = 199, 199 + 1 = 200
200 - 11 = 189, 189 + 1 = 190
190 - 11 = 179, 179 + 1 = 180
180 - 11 = 169, 169 + 1 = 170
170 - 11 = 159, 159 + 1 = 160
160 - 11 = 149, 149 + 1 = 150
150 - 11 = 139, 139 + 1 = 140
140 - 11 = 129, 129 + 1 = 130
130 - 11 = 119, 119 + 1 = 120
120 - 11 = 109, 109 + 1 = 110
110 - 11 = 99, 99 + 1 = 100
100 - 11 = 89, 89 + 1 = 90
90 - 11 = 79, 79 + 1 = 80
80 - 11 = 69, 69 + 1 = 70
70 - 11 = 59, 59 + 1 = 60
60 - 11 = 49, 49 + 1 = 50
50 - 11 = 39, 39 + 1 = 40
40 - 11 = 29, 29 + 1 = 30
30 - 11 = 19, 19 + 1 = 20
20 - 11 = 9, 9 + 1 = 10
10 - 11 = -1 ??????

You can't continue after doing this 24 times. Or you will get -1. As said by @Novarg , you can't take 11 things out of 10 things.

24 times

Assuming I understand your puzzle correctly: You have 250 'things'. Each time you remove 11, you get back one. How many 11s can you remove?

This means that each time you remove 11, you are essentially removing 10. So,

250/10 = 25 removals

• in this case if he has 10 left, how can he remove 11 from 10? – Novarg Mar 16 '15 at 20:06

Agree with @PythonMaster.

But here is another way to look at it without the "...".

If you have 250 "scraps", then for every 11, you can make a new one. There are 22 groups of 11 in 250 with 8 left over. So, from 250, you can use $22\times11=242$, and get 22 new ones.

$$250 - (22\times11) + 22 = 250 - 242 + 22 = 30$$

Now, from these 30, you can get 2 more by using 22.

$$30 - (2\times11) + 2 = 30 - 22 + 2 = 10$$

So, in total, you've made $22+2=24$ new scraps, you've used $242+22=264$ scraps in total, and have 10 left over.