I have to sign these reports and submit the work and dated and I noticed the dates we enter, several days running now, like 3/27/23 is the same backwards but also any date around there like 3/20/23 and so forth. So how many such palindrome dates are there in a year? I can see 4/24/24 is the same and I guess 5/25/25 and so forth but how many are there? I don't want to go over every possibility, is there some equation or such that can pin those numbers down?

Lets go for 2023:
Be aware if we skip the leading zeroes we should do so consistently not allowing palindrome days in years ending in 0.

Using US-notation (m)m/dd/yy. Evidently the yy is fix is 23 so the palindrom date can only be in march and have five digits. 3/2x/23. All ten digits from 0 to 9 are possible. and we have 3/2/23 so the answer is for 23 we have eleven palindrom dates using that notation and skipping leading zeroes. If we include zeroes we have none.

If we use notation as in Europe (at least in several countries) we have (d)d/(m)m/yy be aware if we skip the zeroes we should do so consistently not allowing palindrome days in years ending in 0.

so for 23 we either have none (no 32/11/23) or one 3/2/23.

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