A leap year is one day shorter than a regular year, so it is 365 – 1 = <<365-1=364>>364 days.
Brittany washes her hair every other day, so she will wash it 364 / 2 = <<364/2=182>>182 times in a leap year.
A bottle of shampoo lasts her 14 / 1 / 4 = 14 * 4 = 56 washes.
If she buys 3 bottles, she will only have enough for 56 * 3 = <<3*56=168>>168 washes.
If she buys 4 bottles, she will have enough for 56 * 4 = <<4*56=224>>224 washes.
Since 168 < 182 and 224 > 182, Brittany needs 4 bottles of shampoo to get her through a leap year.
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