# Sugar - cuboid

Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers.
The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet in those three layers were each the same number of cubes. Find out how many cubes had original cuboid. Determine all possibilities.

Correct result:

V1 =  1320
V2 =  1716

#### Solution:

$1320 = 11 \cdot 10 \cdot 12 \ \\ \ \\ 11 \cdot 10 = 10 \cdot (12-1) = (11-1)\cdot (12-1) = 110 \ \\ \ \\ 1716 = 12 \cdot 11 \cdot 13 \ \\ \ \\ 12\cdot 11 = 11\cdot (13-1) = (12-1) \cdot (13-1) = 132$
PHP program:

for($a=1;$a<1000; $a++) { for($b=1; $b<1000;$b++)
{
for($c=1;$c<1000; $c++) {$V = $a*$b*$c; if($V > 2000 || $V<1000) { continue; } if($a*$b == ($c-1)*$b && ($c-1)*$b == ($a-1)*($c-1)) { echo "$V = $a *$b * \$c <br>";
}
}
}
}


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
Tip: Our volume units converter will help you with the conversion of volume units.

## Next similar math problems:

• Sweets, candy
Grandfather gave out sweets to four children. At the last moment, two more children came, so in order to have them all the same, each of the four children would receive four candies less than they would have received if they had not. How much did my grand
• Lottery - eurocents
Tereza bets in the lottery and finally wins. She went to the booth to have the prize paid out. An elderly gentleman standing next to him wants to buy a newspaper, but he is missing five cents. Tereza is in a generous mood after the win, so she gives the m
• Rectangles
Vladimir likes to draw rectangles. Yesterday he created all rectangles that had sides in centimeters and a circumference of 18 cm. How many rectangles of different dimensions have been drawn?
• Rectangles
How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.
• The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
• Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
• TV competition
In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We g
• Average monthly salary
A total of 10 teachers work at one small school in Moravia. The monthly salary of each is 21,500 CZK or 21,800 CZK or 22,500 CZK according to their education and age. The average monthly salary for this school's teacher is 21 850 CZK. How many teachers of
• Two integers
Two integers, a and b, have a product of 36. What is the least possible sum of a and b?
• Math test
In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?
• Red and white
Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the opti
• Apples and pears
Apples cost 50 cents piece, pears 60 cents piece, bananas cheaper than pears. Grandma bought 5 pieces of fruit, there was only one banana and paid 2 euros 75 cents. How many apples and how many pears?
• 600 pencils
600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
• Year 2018
The product of the three positive numbers is 2018. What are the numbers?
• MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
• Chocolate
I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
• Age
In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?