Candy - MO

Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triangle. Gretel wants to distribute sweets so that they get as much as possible, whether Peter trio vertices chosen anyhow. How many such Gretel guaranteed profits?

b) Do the same task even for regular 9-gon to deploy culminating Gretel 1-9 sweets. (equilateral triangles is also isosceles triangles well.)

Correct answer:

a =  21
b =  27

Step-by-step explanation:

$a=1+2+3+4+5+6+7+8-(8+7)=21$

$b=1+2+3+4+5+6+7+8+9-(9+9)=27$

Try another example

Related math problems and questions:

• Pentagon
  Within a regular pentagon ABCDE point, P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
• Katy MO
  Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?
• Octahedron - sum
  On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also
• Z9–I–4 MO 2017
  Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
• Internal angles
  The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
• Camel
  Camel's owner wants to get out of the city into an oasis. He bought 3000 bananas, which wants to sell in the oasis. However, an oasis from the city divided 1,000 kilometers of desert. Camel can carry up to 1000 bananas, and for every kilometer traveled, e
• Amazing number
  An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
• Combi-triangle
  On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
• n-gon
  Gabo draws n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
• 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.
• Tunnels
  Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any
• 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
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
• Interior angles
  In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
• Top of the tower
  The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
• An equilateral
  An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Regular n-gon
  In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.