Japanese Counter Word

I started looking this up after reading this puzzle [0] in The Economist (itself taken from the beginning of Alex Bellos' The Language Lover’s Puzzle Book [1]):

> Now consider this problem, derived from these Japanese phrases: boru niko (two balls), tsuna nihon (two ropes), uma nito (two horses), kami nimai (two sheets of paper), ashi gohon (five legs), ringo goko (five apples), sara gomai (five plates) and kaba goto (five hippos). How do you say “nine cucumbers”? Kyuri kyuhon, kyuri kyuko, kyuri kyuhiki or kyuri kyuto?

[0] https://www.economist.com/books-and-arts/2020/10/31/a-tantal...

[1] https://guardianbookshop.com/the-language-lover-s-puzzle-boo...