As an avid puzzle lover, I enjoyed the range and variety of number, letter, word, geometric, and logic challenges incorporated throughout the book. Most were moderate to high, in terms of difficulty - more challenging than I would have expected for a YA audience. While the puzzles were quite enjoyable, the story lacked a lot, in terms of creativity and believability.
Adult siblings who have spent decades estranged from each other are very unlikely to set aside their differences for a potential $15,000 prize, especially if they already received a large inheritance from their father containing other significant financial resources for them. If parents have botched their parental responsibilities, during the childhood's of their kids, to the point that their offspring are perpetually fighting, too much damage has been done for too long to ever make them long for or enjoy each others' company. As a mental health professional for many decades, I'm keenly aware that chronic turmoil between siblings is nearly always the direct result of chronic friction and marital dissatisfaction between the parents.
In many of these scenarios, one or both of the parents never actually wanted to be a parent, in the first place, so blames the existence of the children and the challenges of raising them on the other spouse. Other chronic marital problems, such as substance abuse, poverty, workaholism, gambling, domestic violence, incest, religious/cultural frictions, sexual incompatibility, and similar destructive patterns often lead to the parents chronically fighting with each other, modeling poor relationship-building and conflict-resolution skills for their offspring, who, then, follow in the footsteps of their primary role models - their parents - but continuing the petty bickering their parents teach them is acceptable within their family.
Clearly, the father of these four Fredrickson siblings took no personal ownership or actions regarding the constant childhood friction between his children, while they were young. Clearly, the major focus of his entire life was his work and his inventions, along with managing his wealth. Since he didn't treat the sibling friction matter seriously when the children were young, his superficial, unrealistic approach attempting to breach the chasms between them, as adults, obviously wasn't going to work.
I'm not sure what happened to their mother nor what her role was, in regards to their upbringing. Perhaps, she died when they were young, leaving them poorly supervised during their young years. The fact she was never mentioned in the book, while several of the father's friends WERE mentioned, seems relevant, to me. Apparently, neither the kids nor their father found her role in the family to be meaningful.
The plot wasn't especially intriguing nor filled with many "red herrings". I knew who the real villains were by midway through the book, which is a rare occurrence with most YA "detective" or "mystery" books. Usually, there are many more twists and turns in the plot. Thus, this book doesn't rate higher than a 3.5 star rating, from me, which I will round upwards to a 4 star review, in light of the challenging puzzles.