matematikk.net

Hvor mange heksaminoer kan bli brettet til en kube?
Finnes det en matematisk måte å regne ut dette på? Det er lett med "prøving og feiling", men finnes det ikke en enklere, mer direkte måte?

Er det ikke maksimum 11 som kan bli brettet til en kube?

Kjemikern wrote:Er det ikke maksimum 11 som kan bli brettet til en kube?

Jepp. Men hvordan kan du vite det?
Finnes det en enklere metode enn å "prøve og feile" - tegne opp alle mulige kombinasjoner..

Drezky wrote:

Kjemikern wrote:Er det ikke maksimum 11 som kan bli brettet til en kube?

Jepp. Men hvordan kan du vite det?
Finnes det en enklere metode enn å "prøve og feile" - tegne opp alle mulige kombinasjoner..

Vet ikke om dette blir enklere, men her er kan det være noe info å hente.
" (c) All of the nets of the cube have the same perimeter. What is this common perimeter? Why is it not the same as the number of edges of a cube?

The nets of the cube all have perimeter 14 (this is easy to check). A cube has 12 edges. The reason these numbers are not the same is that the 14 “outer edges” of a net of the cube do not directly produce the edges of the cube in a one-to-one fashion. Rather, each edge of the cube is formed in one of two ways: either as a fold on an “inner edge” of the net (that is, a dividing line between two adjacent squares in the hexomino), or as a seam between two “outer edges” of the net. Therefore the perimeter of the net, having length 14, contributes exactly seven of the edges of the cube, and the five “inner edges” of the net contribute the remaining five edges of the cube (note that every net of the cube has exactly five “inner edges”). This accounts for all 12 of the edges of the cube."

Kjemikern wrote:

Drezky wrote:

Kjemikern wrote:Er det ikke maksimum 11 som kan bli brettet til en kube?

Jepp. Men hvordan kan du vite det?
Finnes det en enklere metode enn å "prøve og feile" - tegne opp alle mulige kombinasjoner..

Vet ikke om dette blir enklere, men her er kan det være noe info å hente.
" (c) All of the nets of the cube have the same perimeter. What is this common perimeter? Why is it not the same as the number of edges of a cube?

The nets of the cube all have perimeter 14 (this is easy to check). A cube has 12 edges. The reason these numbers are not the same is that the 14 “outer edges” of a net of the cube do not directly produce the edges of the cube in a one-to-one fashion. Rather, each edge of the cube is formed in one of two ways: either as a fold on an “inner edge” of the net (that is, a dividing line between two adjacent squares in the hexomino), or as a seam between two “outer edges” of the net. Therefore the perimeter of the net, having length 14, contributes exactly seven of the edges of the cube, and the five “inner edges” of the net contribute the remaining five edges of the cube (note that every net of the cube has exactly five “inner edges”). This accounts for all 12 of the edges of the cube."

Toppers! Lette etter noe i den dur