There has been sufficient evidence to prove that this claim is true. According to a website by Cognitive Vitality, engaging in mentally stimulating activities can lead to more resistance in later cognitive decline.
The article explained an observational study that examined the association between cognition and word or number puzzle use. The study used 19,078 healthy adults in the UK between the ages of 50 and 93. The article states, "Those who did word or number puzzles at least once a month showed significantly better performance across all cognitive domains compared to those who never used them, and measures of attention were highest in the people who did puzzles most frequently."
This example, along with a lot of other evidence, can conclude that brain games like puzzles can help to slow down cognitive decline, therefore making a person less likely to develop dementia or Alzheimers.
Source: alzdiscovery.org/cognitive-vitality/blog/can-a-puzzle-a-day-keep-dementia-at-bay