A child surrounded by toys who says they are bored is not lying. "Bored" at this age usually means something more specific than the word suggests.
A pile of options is not the same as a plan, and a young child faced with an entire toy shelf can genuinely freeze rather than choose. Naming one specific thing — "build the tallest tower you can" — solves a problem that "go and play" does not.
Sometimes the fix is not a new activity at all. Ten minutes of an adult actually sitting down and playing resets a bored afternoon faster than anything handed over and walked away from.
Not every instance of "I am bored" needs solving by an adult. A little unfilled time is where a child learns to invent their own game, and rescuing every moment of it removes the practice.
Not always — see the point above. A ready activity is useful for the days that are genuinely stuck, not a rule for every complaint of boredom.
Occasional boredom is completely ordinary. If it comes with a broader change in mood or behaviour that concerns you, that is worth raising with your child's doctor or teacher rather than solving with an activity list.
Part of our guide to Filling the unstructured days.