Braingle: 'The Land of Zog' Brain Teaser

The Land of Zog

Math brain teasers require computations to solve.

Puzzle ID:	#199
Fun:	(2.62)
Difficulty:	(1.81)
Category:	Math
Submitted By:	Phyllis
Corrected By:	MarcM1098

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

520

26 (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

mrice Oct 02, 2001	What am I missing? Ten license plates per letter = 260 plates, not 520??
(user deleted) Nov 20, 2001	no mention was made that all numbers are used there could be only ten people in the whole country
admin Mar 11, 2002	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.
newtonmcnay Dec 13, 2003	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.
thebuddhawithin Jul 02, 2004	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)
canu Jul 13, 2004	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.
canu Jul 13, 2004	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.
canu Jul 13, 2004	See the official www.geocities.com/zoggov
darthforman May 25, 2005	???
nkatha23 Nov 09, 2005	never even bothered
Therulerofthem Nov 30, 2005	think it should be changed to what is the maximum number.
SPUTNIK2 Jan 27, 2006	very clever and witty, thanks
solarsistim321 Feb 20, 2006	I DON"T GET IT
keveffect1 Feb 21, 2006	Think through your brain teasers before you submit them please ( it was a decent teaser though
nathalia Mar 07, 2006	yaaa! I got a Math question correct. Great teaser
charles445 Mar 19, 2006	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!
puppehs-rulez Mar 25, 2006	I forgot about the part where you can switch the order so I only got 260...
king_leonard Apr 03, 2006	LOL i only did 1st part meh oh well great teaser by the way LOL
MAroxmysoxonice Apr 03, 2006	i don't care wat any1 else thinx. i thought it was a GREAT teaser!!!!!!!!!!!!!!!!!!!!!
spazzyjazzy93 Apr 05, 2006	ditto petera you never said every single possible license plate number was taken up
dishu May 19, 2006	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
spazzyjazzy93 May 21, 2006	yeah, it is now i like it, good job!
RRAMMOHAN May 27, 2006	I thought the question was clear, and cleverly worded! Got the answer too!
Dishhead5 Aug 13, 2006	cool i do 3-unit maths so pretty easy good one
hsbanana90 Aug 20, 2006	that was pretty easy, i got it. and i think you did a great job with the wording of your question.
senther7 Dec 11, 2006	Zoash bla bla bla....what the... i dont get it, what is "Zog"
Madelulabelle Mar 12, 2007	Ug, you silly peoples! The teaser very plainly said "if ALL of the license plates are used" read the teasers before you trash them.
tintiniscool Apr 22, 2007	Doh! I missed the number zero! Otherwise, I got it right!
jvs13 May 18, 2007	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!
javaguru Jan 28, 2009	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!