Children's game - babcia with grandkids

When I was a kid, my babcia used to play a game with the grandkids. We all held our open hand into the centre of a circle and she would start a Polish rhyme (like the game eenie meenie miney mo) and count our fingers. When she got to the end of the rhyme, the final word sounded like the word PENCE (forgive my pronunciation). We would shout the word and the finger she landed on was put down. She would start the rhyme again and repeat the process until there were 2 fingers left. She would then do a different rhyme to find the last one. The first part sounded like (and again, please forgive my pronunciation) unglisky, punglisky. That is probably not what the words are but I was only a small child. Does anyone recognize this and what is the whole rhyme? I wanted to do it for my grandkids as we used to beg babcia to do the 'finger game'.

The finger game can be the one about a magpie mum which cooked oatmeal for her kids:

Unfortunately, there wasn't enough for all kids.