### Brain Teasers

# The Land of Zog

In the small country of Zog, each person owns one and only one car. Every car's license plate is different and each one contains only one letter and one one-digit number including zero. How many people live in the land of Zog, assuming every license plate is used?

### Answer

52026 (letters of the alphabet) X 10 (1-digit numbers 0-9) = 260

That's only if each letter is before the number, but since it can be after, you have to double that.

260 X 2 = 520

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## Comments

What am I missing? Ten license plates per letter = 260 plates, not 520??

Nov 20, 2001

no mention was made that all numbers are used there could be only ten people in the whole country

The problem does not state that the number or letter must always come first, so "A1" and "1A" are two different valid plates. Thus, the answer is twice 260, or 520. The answer is correct.

This one is simple enough, but it got me. The answer is 520 because the plates could be either Z1 or 1Z. 260 letter-number, 260 number-letter.

It is 520 because the order of the number and letter can be different in two ways, which means there are double 260 ways. (I thought 260 at first also)

The question should be changed to:

"What is the maximum number of persons that can live in the land of Zog"

otherwise there could be even fewer than the ten persons mentioned in the comment by petera.

"What is the maximum number of persons that can live in the land of Zog"

otherwise there could be even fewer than the ten persons mentioned in the comment by petera.

Even with the question changed, there are many difficulties remaining.

The Zog authorities consulted me when the population reached 519, and they were appaled by the prospect of having to put someone to death if two more babies were born without someone dying first.

The obvious solution of adding more letters or digits was ruled out (at least for the next 100 years) by the Zog Constitution, which can only be amended by the unanimous vote of five generations of citizens.

Sending the excess persons into exile was not a solution either, because Zog is surrounded by hostile countries which kill any Zogger who dares to be in, above, or below their territory.

Nevertheless I came up with a solution that would enable Zog to have 818812800 different license plates, while respecting the constitutional requirement of one and only one letter of the 26-letter Roman alphabet and one and only one digit of the decimal system.

The Zog authorities consulted me when the population reached 519, and they were appaled by the prospect of having to put someone to death if two more babies were born without someone dying first.

The obvious solution of adding more letters or digits was ruled out (at least for the next 100 years) by the Zog Constitution, which can only be amended by the unanimous vote of five generations of citizens.

Sending the excess persons into exile was not a solution either, because Zog is surrounded by hostile countries which kill any Zogger who dares to be in, above, or below their territory.

Nevertheless I came up with a solution that would enable Zog to have 818812800 different license plates, while respecting the constitutional requirement of one and only one letter of the 26-letter Roman alphabet and one and only one digit of the decimal system.

See the official www.geocities.com/zoggov

???

never even bothered

think it should be changed to what is the maximum number.

very clever and witty, thanks

I DON"T GET IT

Think through your brain teasers before you submit them please ( it was a decent teaser though

yaaa! I got a Math question correct. Great teaser

Great teaser!

But i have one problem with it.

All the different license plates don't have to be used!

But anyway if you assume all of them must, it's an excellent teaser!

But i have one problem with it.

All the different license plates don't have to be used!

But anyway if you assume all of them must, it's an excellent teaser!

I forgot about the part where you can switch the order so I only got 260...

LOL i only did 1st part meh oh well great teaser by the way LOL

i don't care wat any1 else thinx. i thought it was a GREAT teaser!!!!!!!!!!!!!!!!!!!!!

ditto petera

you never said every single possible license plate number was taken up

you never said every single possible license plate number was taken up

The last line clearly says that every licence plate is used so i dont know what comments are complaining about unless the last line is added only recently

yeah, it is

now i like it, good job!

now i like it, good job!

I thought the question was clear, and cleverly worded! Got the answer too!

cool i do 3-unit maths so pretty easy good one

that was pretty easy, i got it. and i think you did a great job with the wording of your question.

Zoash bla bla bla....what the...

i dont get it, what is "Zog"

i dont get it, what is "Zog"

Ug, you silly peoples! The teaser very plainly said "if ALL of the license plates are used" read the teasers before you trash them.

Doh! I missed the number zero! Otherwise, I got it right!

too bad for the 4 people who has 0-O and O-0 plates and I-1 and 1-I plates.

imagine all the confusion!

imagine all the confusion!

The rating on this is ridiculous.

1.84 difficulty???

2.64 fun???

You've got to be kidding! This is so brain-dead simple it isn't even a teaser! Wake up those brain cells people!

1.84 difficulty???

2.64 fun???

You've got to be kidding! This is so brain-dead simple it isn't even a teaser! Wake up those brain cells people!

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