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If you use Google Chrome there is a cool little extension called Super Mario Flash 1 that you can install from the Google Chrome Extensions library for your kids (or yourself) that lets you play a copied version of Super Mario Bros 3 (I think).
The game opens and has basic arrow key support with space bar being the select or button to fireball your opponents. The game features a ton of levels and even lets you create your own too.
If you are looking to play a simple little Mario game or install something to entertain your younger kids then the Google Chrome Super Mario Flash 1 should help kill some time. The level editor is pretty fun, not only can you create your own levels or levels to challenge your kids, but you can share your levels with others. This adds some replay value if your kids want new levels or you can make easier levels without falls for littler kids.
You can download Super Mario Flash 1 here https://chrome.google.com/webstore/detail/super-mario-flash-1-game/oomnbhaoelhidhnicmacemkkipipngnm