Marinada '23

[lang = hr] U MNM korporaciji smo svi jedna velika sretna obitelj! Na čelu je naš vrhovni otac koji ima dvoje djece. Tako njegova djeca svatko ima po dvoje djece, i svaki od njih ima dvoje svoje djece, i svako od njih ima svoje dvoje djece... i tako 7 generacija (tj. vrhovni otac je 7. predak najmlađoj djeci). Svaka osoba u našoj obitelji također ima najdraži broj između $1$ i $5$. Na obiteljskom okupljanju, svako dijete koje nema svoje djece je primijetilo da njihov omiljeni broj i omiljeni brojevi njihovih predaka redom (do vrhovnog oca) čine palindrom (npr. $12344321$). Na koliko načina su članovi obitelji mogli izabrati svoje omiljene brojeve? [/lang] [lang = en] At MNM corporation, we are all one big happy family! At the head is our supreme father who has two children. So his children each have two children, and each of them has two of his children, and each of them has his two children... and so on for 7 generations (i.e. the supreme father is the 7th ancestor of the youngest children). Each person in our family also has a favorite number between $1$ and $5$. At a family gathering, each child who has no children of their own notices that their favorite number combined with the favorite numbers of their ancestors in order (up to the supreme father) form a palindrome (e.g. $12344321$). In how many ways could family members choose their favorite numbers? [/lang]