Brain Teasers
Cafeteria Capacity
The Madison School has a new cafeteria with very artistic, new tables for its 375 students. Besides the big round tables, some tables are octagons, pentagons, hexagons or squares. The students eat lunch in 3 shifts, with an equal number of students dining during each lunch period. Because the cafeteria is new, they've allowed extra space in case there are more students in the future. Right now, there are 47 empty seats during each lunch period.
Each round table seats ten students. Each of the other types of tables can seat one student on each side.
There are at least 4 tables of each shape.
The same total number of students can be seated at the square tables as at the pentagons, but there are more square tables than pentagons.
The total number of students who can be seated at round tables is equal to the total number of students at the square and pentagon shaped tables combined.
There are more octagonal tables than any other shape.
There is a total of 4 fewer places at the hexagons than at the round tables.
How many tables are there of each shape?
Each round table seats ten students. Each of the other types of tables can seat one student on each side.
There are at least 4 tables of each shape.
The same total number of students can be seated at the square tables as at the pentagons, but there are more square tables than pentagons.
The total number of students who can be seated at round tables is equal to the total number of students at the square and pentagon shaped tables combined.
There are more octagonal tables than any other shape.
There is a total of 4 fewer places at the hexagons than at the round tables.
How many tables are there of each shape?
Hint
Make a chart, and then guess and check to calculate the total number of places at each type of table.Answer
There are 4 round tables, 7 octagonal tables, 6 hexagonal tables, 4 pentagonal tables, and 5 square tables.Table Shape Number of Tables Number of Seats Total Seats
square 5 4 20
pentagon 4 5 20
hexagon 6 6 36
octagon 7 8 56
round 4 10 40
Total places 172
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Comments
that wuz really easy i got it right away
ok thanx for your comment
That was good, but I came up with the answer in a different way:
Round 5x10=50
octagon 8x7=56
pentagon 5x4=20
hexagon 5x6=30
square 4x4=16
Round 5x10=50
octagon 8x7=56
pentagon 5x4=20
hexagon 5x6=30
square 4x4=16
creative solution
Good one; fairly easy, but made me think. I enjoy this type of puzzle. Thanks a lot. (We know that your answer is the only correct one)
Jul 04, 2005
okai. took me awhile, had to write everything down on paper. BUt i got got it! i love problem solving. xept for when you HAVE to do it. lol. anyhoo that was lots of fun. liked it alot. by the way, cute name!
thanx karma
thanks coolperson
especially for the last part of your comment
thanks coolperson
especially for the last part of your comment
i liked it! i like logic grid solvers! their loads of fun! keep em comin flirtmaster!
ONE QUESTION. IS THAT SIGN A FEMALE SIGN OR A MALE SIGN? I GET THEM CONFUSED! srry about the capslock!
ONE QUESTION. IS THAT SIGN A FEMALE SIGN OR A MALE SIGN? I GET THEM CONFUSED! srry about the capslock!
uck! srry comp screwed up!
its ok hotbeaverchick
its a female sign
its a female sign
flirt master, do you like to flirt, or what? ( no offense!!!!!)
flirt master, do you like to flirt, or what? ( no offense!!!!!)
most guys that go to my school say that i flirt with them and i don't even know that im doing it
This had the makings of a good teaser, but fell a little short.
The clue that there are more square tables than pentagons is redundant since they seat the same number. You can eliminate the clue regarding the octagon tables since the next possible solution for the rest of the tables is double the number, which is more than the 172.
Removing the unnecessary information would add a little kick to the teaser.
The clue that there are more square tables than pentagons is redundant since they seat the same number. You can eliminate the clue regarding the octagon tables since the next possible solution for the rest of the tables is double the number, which is more than the 172.
Removing the unnecessary information would add a little kick to the teaser.
I don't get it... Why is the answer 172? Where does that number come from? Shouldn't it be closer to 375... or 422?
172 because only 1/3, 125 eat each shift. It's easy to solve. The least common multiple of 4 and 5 is 20, so the square and pentagon tables each hold a multiple of 20 and the round tables a multiple of 40. Any multiple is too high, so it's 20, 20, and 40. Then the hexagons and octagons are obvious.
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