UnSOLVED: Advanced Yet Accessible Problems in Mathematics
Looking for challenging and engaging math that extends beyond finding answers? UnSOLVED: Advanced Yet Accessible Problems in Mathematics is a series of guided explorations into problems that remain unsolved in the world of mathematics. There are no solutions; they have not been proven true or false. Each book in the series presents a different unsolved problem in an easily accessible context, yet reveals an advanced depth of understanding. Follow along to discover patterns, examine special cases, and learn about these mathematical mysteries. Mathematicians of all ages can participate in these tasks by applying elementary math concepts.
Low Floor: everyone can get on board, simple starting point
High Ceiling: room to grow and stretch beyond the start, not limiting
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UnSOLVED: Number Palindromes
The problem posed in this book elicits the question “Does this always work?” among others. Patterns are revealed as attempts are made to turn numbers 1-100 into palindromes through a guided process. This long-term task is easily accessible for early grade students, yet continues to stump present-day mathematicians. Children and adults will explore patterns, structures, and relationships within this mathematical mystery by applying elementary math concepts. The work leans heavily on the base ten place value system and multi-digit addition. About 80% of all numbers under 10,000 produce a palindrome in four or fewer steps; about 90% of those in seven steps or fewer. What exactly is unsolved in this Number Palindromes problem?
UnSOLVED: Graceful Trees
All trees are graceful. The problem posed in this book explores that statement. While there is a bit of graph theory vocabulary involved, only simple concepts of counting and subtracting are needed to solve these puzzles. Terms are defined, and illustrated examples guide children and adults to apply graceful labeling to tree graphs by placing odd consecutive integers into vertices. Twenty artfully designed trees from our world are presented as a backdrop for examining patterns, strategies, and combinations. What exactly is unsolved in this Graceful Tree problem?
UnSOLVED: Flying Squirrel
The problem posed in this book is one of the most famous open problems in mathematics: the Collatz Conjecture or 3n+1. Patterns, structures, and relationships are explored within the sequences of a simple function. This long-term task is easily accessible for intermediate grade students, yet continues to stump present-day mathematicians. No counterexample nor theorem has been found since 1937 when the problem was first posed. Children and adults are guided through this mathematical mystery with a focus on logic, reasoning, and efficiency, while applying elementary math concepts. The work leans heavily on multiplication, place value, and halving. What exactly is unsolved in this Flying Squirrel problem?
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