Hi there can anyone repair carpets it was burnt by our daughter with her hair dryer it's about 4 inch by1.5 it's so expensive to replace it at its only 18 mths old ant advice would be great

Do you have any off cuts of the carpet ?
Or can a piece be cut out of a area that's not so visible like under a bed or cupboard ?

I would assume a repair would be taking a piece from one area to get the best bland possible. I would imaging carpet is going to be like wall paper with shades due to batch numbers.

I very much doubt a burn is reversible.

Not sure if this will help ?
First result

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So much depends on the style of carpet, a big pattern makes it much more difficult if it is plain then a good match should be relatively easy. Any decent carpet fitter should be able to advise. I assume your home insurance does not cover accidental damage.