Is it permissible to simultaneously fast one of the six days of the month of Shawwaal and one of the three white days of the same month (13th, 14th, and 15th)?

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If a day of the six days of Shawwaal coincides with a day of the white days, then a person may make the intention to combine both days in one fast, and his fast of both days is valid. According to Tuhfat Al-Habeeb:

Two voluntary fasts may overlap on the same day, such as the occurrence of the day of ‘Arafah or the day of ‘Aashooraa’ on a Monday or Thursday. The same happens when a day of the six days of Shawwaal takes place on a Monday or Thursday. In this case, fasting becomes more recommended given that the two occasions are on the same day. If a person makes the intention to observe both, then his fast is valid for both days.

In his commentary on Tuhfat Al-Muhtaaj, Ibn al-Qaasim says:

One may argue that the person needs to make a separate intention for every regular voluntary fast that he observes, such as the day of ‘Arafah, the day of ‘Aashooraa’, the white days of every lunar month, and the six days of Shawwaal, just as one is required to do so for regular voluntary prayers. However, this is refuted by the fact that fasting on such days is observed in consideration of them in principle. Rather, if one combines another fasting occasion with them, then both are valid. This issue is similar to that of the tahiyyat-ul-masjid (2 units of prayer that are prayed when entering the mosque before sitting down) prayer. This is because what is basically required is that the person fasts on such days no matter what the intention is made for. [Slightly adapted]

Allaah Knows best.