Alternative word for "run into" (to meet by chance)

Winwin2011 said:

What is an alternative word for "run into" (to meet by chance: ran into an old friend)? I couldn't find it from dictionaries.
Could anybody help me, please?

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Why do you need an alternative?

bhaisahab said:

Why do you need an alternative?

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Thanks bhaisahab

Run into is a phrasal verb. I think phrasal verbs are difficult for non-native children to remember. Children might write "I ran in an old friend last Sunday"

You could "happen upon" somebody.

***** NOT A TEACHER *****

I communicated with Professor Google, who gave me these results:

run into
bump into
chance upon
run across
come across
happen upon

If you're writing for kids, why not use "saw" or "met"?