### Brain Teasers

# Kebab Farmer

In the legendary country of MADADIA, there once lived a kebab farmer. One day, he had 1000 freshly grown Kebabs to package and 10 empty boxes into which to put them.

He asks his assistant Norris O'Cabbage to place all the one thousand Kebabs in all the 10 boxes in such a manner that if a customer asks for any number of Kebabs from 1 to 1000, Norris should be able to pick them in terms of boxes.

How did Norris O'Cabbage place all the Kebabs among the ten boxes, given that any number of freshly harvested Kebabs can be put in one box.

He asks his assistant Norris O'Cabbage to place all the one thousand Kebabs in all the 10 boxes in such a manner that if a customer asks for any number of Kebabs from 1 to 1000, Norris should be able to pick them in terms of boxes.

How did Norris O'Cabbage place all the Kebabs among the ten boxes, given that any number of freshly harvested Kebabs can be put in one box.

### Answer

1, 2, 4, 8, 16, 32, 64, 128, 256, 489Let's start from scratch.

The Kebab farmer can ask for only 1 Kebab, so one box must contain 1 Kebab.

He can ask for 2 Kebabs, so one box must contain 2 Kebabs.

He can ask for 3 Kebabs, in which case box one and box two will add up to 3 Kebabs.

He can ask for 4 Kebabs, so one box, i.e. a third box, must contain 4 Kebabs.

Now using box number one, two and three containing 1, 2 and 4 Kebabs respectively, Norris can give up to 7 Kebabs. Hence, the fourth box must contain 8 Kebabs.

Similarly, using first four boxes containing 1, 2, 4 and 8 Kebabs, Norris can give up to 15 Kebabs. Hence, the fifth box must contain 16 Kebabs.

You must have noticed one thing: that each box till now contains power of 2 Kebabs. Hence the answer is 1, 2, 4, 8, 16, 32, 64, 128, 256, 489. This is true for any number of Kebabs.

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## Comments

The answer is fine, but the reasoning is a little off.

The reason that you have a box of 2 isn't that that's the only

way to get a total of two (you could have two boxes of 1 each),

it's that if you start that way, you will need more than 10 boxes.

Powers of two gives you the most efficient way to get to a given

total with the minimum number of boxes, but when there's a little

slack (as there is here, with only 1000 kebabs), you can get away

with slightly less than the power of two in some boxes.

For example, another solution is: 1, 2, 4, 8, 16, 31, 63, 125, 251, 499.

The main restriction is that if the numbers are sorted into increasing order

(as they are here), each number can be at most the sum of the previous numbers plus one.

Beyond that, it's just a matter of making sure the solution fits in 10 boxes.

If any of the first 5 numbers are changed, the solution won't fit.

The reason that you have a box of 2 isn't that that's the only

way to get a total of two (you could have two boxes of 1 each),

it's that if you start that way, you will need more than 10 boxes.

Powers of two gives you the most efficient way to get to a given

total with the minimum number of boxes, but when there's a little

slack (as there is here, with only 1000 kebabs), you can get away

with slightly less than the power of two in some boxes.

For example, another solution is: 1, 2, 4, 8, 16, 31, 63, 125, 251, 499.

The main restriction is that if the numbers are sorted into increasing order

(as they are here), each number can be at most the sum of the previous numbers plus one.

Beyond that, it's just a matter of making sure the solution fits in 10 boxes.

If any of the first 5 numbers are changed, the solution won't fit.

That is all well and good, and I appreciate your comments. There is more than one answer obviously, but I only need to put one. I never said that this was the only answer, just my answer. Lots of teasers have several answers, unfortunately we don't alway list every one, just the ones we know, or the one we find the easiest.

You sure do like your kebabs, don't you mad-ade?

WHAT ARE KEBABS?!!!

seems that all ur legendary places are named after u

mad ade i got a question for you are your kabobs in england like the ones here in the us, just wondering we make ours basically with pork and vegtables. just a question, if you would like my email is georgee1978@yahoo.com talk to you then

Its your answer or one that you just got from somewhere else like here http://www.hehe.at/funworld/archive/1211.html ??

Its a simple application of a binomial expansion, but of coarse you knew this already!

Its a simple application of a binomial expansion, but of coarse you knew this already!

The answer is a basic answer, probably found on many sites across the web, it is basic math after all. All I did was apply the math to a teaser of my own design. Any one could do it, its not hard. In fact it is easier than just roaming around a website into which you have not imputted anything and critising those who try to make the site entertaining for others!

Mad, you are about as entertaining as watching paint dry, you are such a hypocrite,you put down other peoples teasers also!!are they treading on your toes.Oh and by the way your crappy little country is MYTHICAL not LEGENDARY. A legend has partial truth!

Nope, it is definately LEGENDARY!

Imagine the look on the customer's face when he asks for 15 kebabs, and is given 4 boxes, with 8, 4, 2, and 1 kebab inside each. And EACH of these boxes is large enough to hold at least 489 kebabs! XD In fact, the boxes are apparently infinitely large (or else the kebabs are infinitely small), as mad-ade states that "any number" of kebabs can fit in one.

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