The short answer is many more times than most parents expect, and far more than most of us manage before quietly giving up on a food.
The number
Repeated offering is really boring, but we know that some children need something like 15 to 20 exposures to a food. For certain children it is an awful lot more than that.
Set against that, three or four attempts is nothing. If you have offered a food a handful of times and concluded your child does not like it, you have most likely stopped somewhere in the early part of the process.
Why it takes that long
Eating is a very complex sensory task. It involves all of the senses, not just smell and taste, but touch, sound, balance and coordination, body awareness and internal cues.
Adults subconsciously know what to expect from foods. Children are still learning what to expect, and that learning happens through repeated encounters. Each offer builds a bit more familiarity, even the ones where nothing is eaten.
It also helps to know that most toddlers go through a phase of food neophobia from around 18 months to 2 years, where previously accepted foods start being refused and new foods are rejected. Repetition is how you work with that phase rather than against it.
How to keep offering without applying pressure
This is the part that matters, because repetition with pressure attached does not help.
Ignore refusal
If the food is refused, ignore it and keep calm. No commentary, no negotiation.
Watch your language
Avoid just take one more bite, try a tiny bit, or you had it last week so why not now. These sound harmless but can be perceived as pressure. Rewards or praise for finishing everything should also be avoided.
Use neutral descriptions
Describe a food as crunchy rather than yummy. Yummy is your opinion. If your child has a strong reaction, you can acknowledge it with something like, that was a strong taste for you, which helps them feel heard.
Try a side plate
Offering new foods on a side plate works for some children. So does self serve, family style eating, where nothing is automatically portioned up and it is a bit more help yourself. Lots of nurseries do this.
Do not hide it
Generally I would not hide foods. Children need to see what a food actually looks like. Sauces with vegetables naturally in them are fine, but if that is the only way you ever offer them, your child never becomes familiar with the vegetable itself.
Keep rotating the foods they already accept
This is an important one if you think you have a fussy eater. Rotate the foods they do like, so they do not get really stuck on a small number of them.
The risk otherwise is that a food gets eaten every day, then dropped, and you are left short with nothing to fall back on.
Avoid the rescue meal
Try to resist the urge to top up with preferred foods. Know that you will be offering food again not too much later. If you keep offering a rescue meal, or something you know they like, it often backfires and makes it harder to get them to take what you are actually offering.
The same goes for grazing throughout the day. Over the age of one, snacks two to three times a day between meals are fine, and worth seeing as an additional nutrient opportunity. Constant grazing is different.
Where the exposures happen matters too
Nurseries are genuinely good at this. There is a lot of positive role modelling, children sit around the same table and watch their peers and caregivers eating the same foods, and mealtimes are consistent and predictable.
Carefully planned rotational menus help as well, because they give children repeated exposure to foods without meals becoming repetitive. Every few weeks the same types of meals come round again, which is exactly the kind of repetition that builds acceptance.
When to stop counting and get advice
Repetition is the answer for typical fussiness. It is not the answer for everything. If your child is eating fewer than 20 foods in total, omitting whole food groups, or gagging and vomiting in a way that is not resolving after several weeks, that is worth getting looked at rather than persisting alone.
