Við teljum blóm á kortinu til skemmtunar.

til skemmtunar is an adverbial phrase expressing purpose – it means “for fun.” In Icelandic, til used in this sense always takes a noun in the genitive. Hence skemmtun (entertainment, fun) becomes skemmtunar.

Yes. til gamans is a very common alternative meaning “for fun.”

• gaman (“fun, amusement”) also appears in the genitive after til: hence til gamans.
• til skemmtunar is slightly more formal or literary, but they are interchangeable in everyday speech.

The preposition á can govern either accusative or dative in Icelandic, depending on meaning:

• Dative after á denotes location (“on something”).
• Accusative after á denotes motion toward a surface (“onto something”).

Here we are talking about where the counting takes place (“on the map”), so we use dative: á + kortinu (the dative singular of kort).

In Icelandic you count “on” a map, so the usual preposition is á.

• á korti = on a map
• í korti would more likely mean “inside a card” or “within a chart,” and is not used for maps.

Preposition choice often differs from English.

blóm is a neuter noun. In Icelandic, neuter nouns have identical forms for nominative and accusative in both singular and plural.

• Singular: blóm (nom) / blóm (acc)
• Plural: blóm (nom) / blóm (acc)

So blóm serves as the object in the accusative here without any extra ending.

The verb telja can mean both “to count” and “to consider/regard,” but context decides.

• “Við teljum blóm á kortinu til skemmtunar” clearly means “We’re counting the flowers on the map for fun.”
• You would need a different construction to say “consider,” often with a reflexive or passive: e.g. hann telst (he is considered).

In Icelandic the verb ending -um already marks first person plural, so you can drop við in casual speech and still know who’s doing it. For example:

• Teljum blóm á kortinu til skemmtunar.
  However, using við adds clarity or emphasis, especially in writing or formal speech.