Friday Puzzle #42 - So Long, and Thanks for All the TomTom
With jdyer triggering a planned stopping mechanism for the 2010 project - I was wondering how long I could go until someone complained about the repetition of the format and the answer was 12 weeks - the Friday Puzzle series is moving on to other things for awhile. I'd still like to make "classic" versions of Akari and Fillomino and a few other standards that I did not hit, but they will use other themes when I get around to constructing them. Whatever you thought of the 2010 project, I hope I demonstrated how just about all logic puzzles can be themed in simple but interesting ways. And even though you knew what would be coming each week, I hope that I executed some memorable puzzles and some unexpected theme mechanisms along the way. Still, its time to bid this winter project adieu.
To usher in the spring, I wanted to follow up on a discussion that happened with my "anniversary" TomTom a few weeks ago. Basically, a commenter asked if I'd explored varied number sets since 1-N does not always form the best set of digits for some types of operations such as repeated division or subtraction. Consider a set like {1,2,3,4,6,9} where there is a much more balanced division and multiplication space since there are no factors sticking out like 5 or 7 in 1-N sets over normal sizes. Addition and subtraction also behave differently in this set since a whole new set of two-cell values turn out to be unique like a sum of 8 or 9. There are also many more multi-cell subtraction possibilities since the range of digits is broadened.
As I answered in that earlier entry, I did explore this concept in my upcoming Calcu-doku book using number sets like the first 6 primes or the first 6 Fibonacci numbers (including duplicated ones which itself is a fun change). There are nowhere near as many of these variations as the standard 1-N puzzles in the book, but these novel challenges form a great concluding section to a book intended to have both broad appeal and good difficulty progression. Still, since I'm the only one doing much innovation with calcu-doku puzzles these days, I figured it was time to provide some TomTom puzzles here with varied number sets to show how they can stretch the mathematical thinking in new directions. Both of the following puzzles exploit a particular kind of theme where all cage values are members of the number set, but there are many many more things you can do in this puzzle-space as you'll find out later this year both here and in my book.
Rules: Place a single number into each cell from the indicated set below the puzzle so that each number appears exactly once in every row and column. There are bold cages in each grid, each with an indicated value that must be the result of a single operation (+, -, x, /) performed successively on the numbers in that cage, starting with the largest value for division/subtraction. In the first puzzle, the operations are not given to you, but at least one operation exists that gives the indicated value when applied to the numbers in the cells. For example, a three-cell cage with the value 2 could contain the digits 4, 2, 1 in some order since 4/2/1 (or 4/1/2) = 2 but it could not have the digits 4, 3, 1 since there is no expression amongst (4+3+1, 4x3x1, 4-3-1, 4/3/1) that gives the value 2.
To usher in the spring, I wanted to follow up on a discussion that happened with my "anniversary" TomTom a few weeks ago. Basically, a commenter asked if I'd explored varied number sets since 1-N does not always form the best set of digits for some types of operations such as repeated division or subtraction. Consider a set like {1,2,3,4,6,9} where there is a much more balanced division and multiplication space since there are no factors sticking out like 5 or 7 in 1-N sets over normal sizes. Addition and subtraction also behave differently in this set since a whole new set of two-cell values turn out to be unique like a sum of 8 or 9. There are also many more multi-cell subtraction possibilities since the range of digits is broadened.
As I answered in that earlier entry, I did explore this concept in my upcoming Calcu-doku book using number sets like the first 6 primes or the first 6 Fibonacci numbers (including duplicated ones which itself is a fun change). There are nowhere near as many of these variations as the standard 1-N puzzles in the book, but these novel challenges form a great concluding section to a book intended to have both broad appeal and good difficulty progression. Still, since I'm the only one doing much innovation with calcu-doku puzzles these days, I figured it was time to provide some TomTom puzzles here with varied number sets to show how they can stretch the mathematical thinking in new directions. Both of the following puzzles exploit a particular kind of theme where all cage values are members of the number set, but there are many many more things you can do in this puzzle-space as you'll find out later this year both here and in my book.
Rules: Place a single number into each cell from the indicated set below the puzzle so that each number appears exactly once in every row and column. There are bold cages in each grid, each with an indicated value that must be the result of a single operation (+, -, x, /) performed successively on the numbers in that cage, starting with the largest value for division/subtraction. In the first puzzle, the operations are not given to you, but at least one operation exists that gives the indicated value when applied to the numbers in the cells. For example, a three-cell cage with the value 2 could contain the digits 4, 2, 1 in some order since 4/2/1 (or 4/1/2) = 2 but it could not have the digits 4, 3, 1 since there is no expression amongst (4+3+1, 4x3x1, 4-3-1, 4/3/1) that gives the value 2.