Nintendo can brick your 3DS - confirmed.

Top of the FSF's list of complaints, for example, is that the device's TOS "makes a threat that Nintendo will brick your device if you use your 3DS in a way that they do not approve," Gay explained.
Specifically, wording in the document states that Nintendo "may update or change the Nintendo 3DS System or the Nintendo 3DS Service in whole or in part, without notice to you," he wrote.
Following such an update, "any existing or future unauthorized technical modification of the hardware or software of your Nintendo 3DS System, or the use of an unauthorized device in connection with your system, will render the system permanently unplayable," he explained, quoting Nintendo's wording.

 A campaign launched against Nintendo's terms of service has given us confirmation about Nintendo's ability to brick any 3DS system they want. Additionally, it seems Nintendo is keeping track of a lot of 3DS user data, much to the dislike of many, including the group's campaign manager, Joshua Gay.

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