1. An apparatus to solve sudoku comprising a gameboard and a plurality of tokens; said gameboard comprising:
a plurality of horizontally disposed rows and vertically disposed columns organized into a grid;
said grid comprising a plurality of boxes;
each said box comprising a plurality of cells;
means to distinguish each said box from other said boxes;
said tokens being divided into groups, one said group of tokens corresponding to each said box, means to associate each said group of tokens with one said box, a number of tokens in each said group equaling a number of cells in a box with which said group of tokens is associated, each said token comprising a token identifier to distinguish said token from other said tokens in its group.
2. The apparatus to solve sudoku of claim 1 wherein each said token comprises a token setup side and a token playing side, and means to distinguish between said token setup side and said token playing side.
3. The apparatus to solve sudoku of claim 2 wherein a height of each said row is substantially equal to a width of each said column, and each said token is sized such that a minimum of substantially one and a half tokens fits within the height of each said row or within the width of each said column.
4. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said row and means of identifying each said column.
5. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said box.
6. The apparatus to solve sudoku of claim 2 wherein said gameboard further comprises means of identifying each said row of boxes and means of identifying each said column of boxes.
7. The apparatus to solve sudoku of claim 2 wherein said means to distinguish each said box from other said boxes is a color assigned to each said box, each said box being marked with a different color; and wherein said means to associate each said group of tokens with one said box is the color assigned to the box which said group of tokens is associated with, each said token within said group of tokens being marked with said color.
8. The apparatus to solve sudoku of claim 7 wherein said token identifiers within a given group of tokens are ascending token numbers, the lowest said token number equaling 1 and the highest said token number equaling the number of cells in the box with which said given group of tokens is associated.
9. The apparatus to solve sudoku of claim 4 wherein said means of identifying each said row comprises capital letters, and wherein said means of identifying each said column comprises small case letters.
10. The apparatus to solve sudoku of claim 5 wherein said means of identifying each said box comprises capital letters.
11. The apparatus to solve sudoku of claim 6 wherein said means of identifying each said row of boxes comprises Roman numerals, and wherein said means of identifying each said column of boxes comprises Roman numerals.
12. The apparatus of claim 2 wherein said means to distinguish between said token setup side and said token playing side comprises a solid ring around an edge of each said token setup side.
13. The apparatus to solve sudoku of claim 1 further comprising a breakthrough board and a marker, said breakthrough board comprising a breakthrough board grid permanently marked on it, a layout of said breakthrough board grid corresponding to a layout of the gameboard grid, said marker being an erasable marker whereby markings made by said marker on said breakthrough board are quickly and easily erased.
14. The apparatus to solve sudoku of claim 13 further comprising, on said breakthrough board, means of identifying each said row and means of identifying each said column.
15. The apparatus to solve sudoku of claim 14 further comprising, on said breakthrough board, means of identifying each said row of boxes and each said row of columns in said breakthrough board grid.
16. The apparatus to solve sudoku of claim 1 further comprising a sudoku play nomenclature system comprising a row identifier identifying each row in said grid; a column identifier identifying each column in said grid; a means of identifying boxgroup identifier identifying each said box and its associated group of tokens; a token identifier identifying each token within each said group of tokens; and the conventions that each said cell is identified by its row identifier and its column identifier, each said token is identified by its token identifier and its boxgroup identifier, and that notation in the form xy>Jj means that a token of token identifier x of group y is moved to the cell located at an intersection of row J and column j.
17. The apparatus to solve sudoku of claim 16 wherein said sudoku play nomenclature further comprises the conventions that xy>JjKk means that a token of token identifier x of group y is moved to a position straddling cells Jj and Kk, that xy>JjKkMm means that a token of token identifier x of group y is moved to a position straddling cells Jj, Kk and Mm, and that xy>JjKkMmNn means that a token of token identifier x of group y is moved to a position straddling cells Jj, Kk, Mm, and Nn.
18. The apparatus to solve sudoku of claim 17 wherein said sudoku play nomenclature further comprises the conventions that xy>J means that a token of token identifier x of group y is moved to a head or foot of row J, that xy>j means that a token of token identifier x of group y is moved to a head or foot of column j, that xy>JK means that a token of token identifier x of group y is moved to a location straddling the head or foot of row J and a head or foot of row K, that xy>jk means that a token of token identifier x of group y is moved to a head or foot of column j and the head or foot of column k, and that xy>Q means that a token of token identifier x of group y is moved into a queue off the gameboard associated with group y.
19. The apparatus to solve sudoku of claim 13 further comprising a sudoku play nomenclature system comprising a row identifier identifying each row in said breakthrough board grid; a column identifier identifying each column in said breakthrough board grid; a means of identifying each breakthrough board box; and the convention that each said breakthrough board cell is identified by its row identifier and its column identifier, and that notation in the form xy>Jj means that \u201cx\u201d should be erasably inscribed in breakthrough board cell Jj in breakthrough board box y.
20. A method to solve a sudoku puzzle comprising the steps of:
A. Providing a sudoku puzzle to be solved having setup identifiers in some of its cells; and an apparatus to solve sudoku comprising a gameboard and a plurality of tokens;
said gameboard comprising:
a plurality of horizontally disposed rows and vertically disposed columns organized into a grid;
said grid comprising a plurality of boxes;
each said box comprising a plurality of cells;
means to distinguish each said box from other said boxes;
said tokens being divided into groups, one said group of tokens corresponding to each said box, means to associate each said group of tokens with one said box, a number of tokens in each said group equaling a number of cells in a box with which said group of tokens is associated, each said token comprising a token identifier to distinguish said token from other said tokens in its group, a token setup side, and a token playing side, and means to distinguish between said token setup side and said token playing side; and
B. Performing a setup step by emplacing one said token, setup side up, in each gameboard cell corresponding to a cell in said sudoku puzzle to be solved with contains a setup identifier, each said token thus emplaced having a token identifier same as the setup identifier in the corresponding cell in the sudoku puzzle to be solved, each token thus emplaced being emplaced in the box with which said token is associated.
21. The method to solve a sudoku puzzle of claim 20 comprising the further filling-the-boxes steps of:
C. Emplacing one said token playing side up in a gameboard cell in the box with which said token is associated if such cell is the only possible destination for said token in accordance with conventional sudoku rules.
D. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two adjacent or tangential gameboard cells in the box with which said token is associated, emplacing said token playing side up straddling said two adjacent or tangential gameboard cells;
E. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into three adjacent gameboard cells sharing a common corner in the box with which said token is associated, emplacing said token playing side up straddling said three adjacent gameboard cells; and
F. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into four adjacent cells sharing a common corner in the box with which said token is associated, emplacing said token playing side up straddling said four adjacent cells.
22. The method to solve a sudoku puzzle of claim 21 comprising the further filling-the-boxes steps of:
G. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said row, emplacing said token playing side up at a head or foot of said row;
H. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said column, emplacing said token playing side up at a head or foot of said column;
I. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said rows, emplacing said token playing side up straddling the heads or feet of said rows;
J. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said columns, emplacing said token playing side up straddling the heads or feet of said columns;
K. Where one said token cannot be emplaced as described above, emplacing said token in queue off said gameboard.
23. The method to solve a sudoku puzzle of claim 22 comprising the further steps of:
L. Providing a breakthrough board and an erasable marker, whereby marks made by said erasable marker are quickly and easily erased from said breakthrough board;
M. Permanently printing on said breakthrough board a breakthrough board grid of a same layout as said gameboard grid;
N. Erasably inscribing in the cells of said breakthrough board all the possible token identifiers which can go into said breakthrough board cells, determined in accordance with conventional sudoku rules; and
O. Finding a breakthrough move in accordance with conventional sudoku rules by scrutinizing the inscribed breakthrough board.
24. The method to solve a sudoku puzzle of claim 23 comprising the further step of erasing said possible token identifiers from said breakthrough board, whereby said breakthrough board is rendered ready to be used again.
25. The method to solve a sudoku puzzle of claim 23 comprising the further steps of:
P. Where no said breakthrough move can be found, scrutinizing said breakthrough board for a best cell with which to make a trial-and-error attempt; and
Q. Making said trial-and-error attempt on said gameboard.
26. The method to solve a sudoku puzzle of claim 25 comprising the further steps of:
R. Where said trial-and-error attempt fails, removing from said gameboard the tokens bearing said possible token identifiers inscribed on said breakthrough board; and
S. Emplacing said removed tokens on or around said gameboard as described in steps D through K above, whereby said gameboard is restored to a configuration same as prior to the failed trial-and-error attempt.
27. An apparatus to solve sudoku comprising a gameboard and tokens, said gameboard comprising a 9\xd79 sudoku grid divided into nine 3\xd73 boxes of nine cells each and means of mutually distinguishing said boxes; said tokens being divided into nine groups of nine tokens each, and means of associating each said group of tokens with a unique said box.
28. The apparatus to solve sudoku of claim 27 wherein each said token comprises a token setup side and a token playing side, and means to distinguish between said token setup side and said token playing side.
29. The apparatus to solve sudoku of claim 28 wherein a height of each said row is substantially equal to a width of each said column, and each said token is sized such that at least one and a half tokens fits within the height of each said row or within the width of each said column.
30. The apparatus to solve sudoku of claim 27 wherein said means of mutually distinguishing said boxes comprises a unique color in each said box, and wherein said means of associating each said group of tokens with a given said box comprises color on said group of tokens substantially the same as the color of the given said box with which said group of tokens is associated.
31. The apparatus to solve sudoku of claim 30 further comprising a row identifier associated with each said row, a column identifier associated with each said column, and a box identifier associated with each said box.
32. The apparatus to solve sudoku of claim 27 further comprising a breakthrough board permanently inscribed with a 9\xd79 sudoku grid divided into nine 3\xd73 boxes of nine cells each, and means of erasably writing on the breakthrough board grid.
33. The apparatus to solve sudoku of claim 32 wherein said means of erasably writing on the breakthrough board grid comprises a dry-erase marker, and breakthrough board material suitable for inscription by a dry-erase marker.
34. The apparatus to solve sudoku of claim 32 further comprising a row identifier associated with each said breakthrough board row, and a column identifier associated with each said breakthrough board column.
35. A method to solve a sudoku puzzle comprising the steps of:
A. Providing a sudoku puzzle to be solved; and an apparatus to solve sudoku comprising a gameboard and tokens, said gameboard comprising a 9\xd79 sudoku grid divided into nine rows, nine columns, nine 3\xd73 boxes of nine cells each, each said box bearing a unique color, a row identifier associated with each said row, a column identifier associated with each said column; said tokens being divided into nine groups of nine tokens each, a color on each said group of tokens substantially the same as the color of one said box with which such group of tokens is associated, the nine said tokens within each said group bearing a token number ranging between 1 and 9 respectively on a token setup side and a token playing side; and
B. Performing a setup step by emplacing one said token, setup side up, in each gameboard cell which corresponds to a setup cell in said sudoku puzzle to be solved containing a setup number, each said token thus emplaced having a token number same as the setup number in the sudoku puzzle cell corresponding to the gameboard cell in which the setup token is emplaced.
36. The method to solve a sudoku puzzle of claim 35 comprising the further steps of:
C. When each said token is emplaced on said gameboard as described below, emplacing each said token with its playing side up;
D. Emplacing one said token in a gameboard cell if such cell is the only possible destination for said token in accordance with conventional sudoku rules;
E. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two adjacent or tangential gameboard cells, emplacing said token straddling said two adjacent or tangential gameboard cells;
F. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into three adjacent gameboard cells which share a common corner, emplacing said token straddling said three adjacent gameboard cells;
G. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into four adjacent cells sharing a common corner, emplacing said token straddling said four adjacent cells;
H. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said row, emplacing said token at a head or foot of said row;
I. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into a single said column, emplacing said token at a head or foot of said column;
J. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said rows, emplacing said token straddling the heads or feet of said rows;
K. Where it can be determined in accordance with conventional sudoku rules that one said token can only go into two said columns, emplacing said token straddling the heads or feet of said columns;
L. Where one said token cannot be emplaced as described above, emplacing said token off said gameboard in queue;
M. Continuing to solve said sudoku puzzle in accordance with conventional sudoku rules, with each play moving said tokens as appropriate into home cells and into progressively more restricted positions on said gameboard, until all said tokens have been moved into respective cells, and said sudoku game is solved.
37. The method to solve a sudoku puzzle of claim 36 comprising the further steps of:
N. Providing a breakthrough board upon which numbers can be erasably written;
O. Permanently printing on said breakthrough board a breakthrough board grid of the same layout as said gameboard grid;
P. Erasably writing in corresponding cells of said breakthrough board all possible token numbers which can go into said gameboard board cells determined in accordance with conventional sudoku rules; and
Q. Finding a breakthrough move in accordance with conventional sudoku rules by scrutinizing the inscribed breakthrough board.
38. The method to solve a sudoku puzzle of claim 37 comprising the further step of erasing said possible token identifiers from said breakthrough board, whereby said breakthrough board is rendered ready to be used again.
39. The method to solve a sudoku puzzle of claim 37 comprising the further steps of:
R. Where no said breakthrough move can be found, scrutinizing said breakthrough board for a best cell with which to make a trial-and-error attempt; and
S. Making said trial-and-error attempt on said gameboard.
40. The method to solve a sudoku puzzle of claim 39 comprising the further steps of:
T. Where said trial-and-error attempt fails, removing from said gameboard the tokens bearing said possible token identifiers inscribed on said breakthrough board; and
U. Emplacing said removed tokens on or around said gameboard as described in steps C through L above, whereby said gameboard is restored to a configuration same as prior to the failed trial-and-error attempt.
41. The method to solve a sudoku puzzle of claim 22 comprising the further steps of continuing to solve said sudoku puzzle in accordance with conventional sudoku rules, with each play moving said tokens as appropriate into home cells and into progressively more restricted positions on said gameboard, until all said tokens have been moved into respective cells, and said sudoku game is solved.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A jounce bumper made of elastomeric thermoplastic material, comprising:
a hollow elongated tubular body having a wall, the tubular body having at least two bellows, each bellow being defined by a peak and a trough, the peak having a fillet radius of rs, the trough having a fillet radius of rc and a maximum wall thickness in the trough of Tmax; wherein rc is greater than rs, and wherein the ratio of Tmax, the maximum thickness of the wall in a trough to Tm, the thickness of the wall at an intermediate point between the peak and the trough, is greater than or equal to 1.2, and wherein the trough is defined by a wall arc having end points Tm.
2. A jounce bumper according to claim 1, wherein (TmaxTm), the ratio of maximum wall thickness in the trough to the thickness of the wall at an intermediate point, is greater than (TmaxTm)1,
wherein (TmaxTm)1=3.43\u22120.05 P\u22120.222 SQRT (95\u22124.19 P+0.05P2\u22120.23Ri), where
Tmax is the maximum wall thickness at a trough;
Tm is the wall thickness at the point of tangency between a circle of radius rc and a circle of radius rs, or if rs and rc are not tangent, Tm is the wall thickness at the midpoint of a line drawn tangent to circles rs and rc;
SQRT is square root;
P is the pitch; and
Ri is the external radius at a trough.
3. A jounce bumper according to claim 1 comprising a thermoplastic elastomer that has a melt viscosity between 0.5 and 8 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
4. A jounce bumper according to claim 2 comprising a thermoplastic elastomer that has a melt viscosity between 0.5 and 8 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
5. A jounce bumper according to claim 1 comprising a thermoplastic elastomer that has a melt viscosity between 2 and 6 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
6. A jounce bumper according to claim 2 comprising a thermoplastic elastomer that has a melt viscosity between 2 and 6 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
7. A jounce bumper according to claim 1 comprising a thermoplastic elastomer that has a melt viscosity between 3 and 5 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
8. A jounce bumper according to claim 2 comprising a thermoplastic elastomer that has a melt viscosity between 3 and 5 g10 minutes, at 230\xb0 C. under 5 kg load measured according to ISO1133, and a hardness between at or about 45 and 60D measured at 1 s according to ISO868.
9. A jounce bumper according to claim 1 comprising a thermoplastic elastomer that is selected from the group consisting of copolyetheresters and copolyesteresters that are copolymers having a multiplicity of recurring long-chain ester units and short-chain ester units joined head-to-tail through ester linkages, said long-chain ester units being represented by formula (A):
and said short-chain ester units being represented by formula (B):
wherein
G is a divalent radical remaining after the removal of terminal hydroxyl groups from poly(alkylene oxide)glycols having preferably a number average molecular weight of between about 400 and about 6000; R is a divalent radical remaining after removal of carboxyl groups from a dicarboxylic acid having a molecular weight of less than about 300; and
D is a divalent radical remaining after removal of hydroxyl groups from a diol having a molecular weight preferably less than about 250; and
wherein said copolyetherester(s) preferably contain from about 15 to about 99 wt-% short-chain ester units and about 1 to about 85 wt-% long-chain ester units.
10. A method for the manufacture of a jounce bumper, comprising the step of:
shaping elastomeric thermoplastic material into a hollow elongated tubular body having a wall, the tubular body having at least two bellows, each bellow being defined by a peak and a trough, the peak having a fillet radius of rs, the trough having a fillet radius of rc and a maximum wall thickness at the trough of Tmax; wherein rc is greater than rs, and wherein the ratio of Tmax, the maximum thickness of the wall at a trough, to Tm, the thickness of the wall at an intermediate point between peak and trough, is greater than or equal to 1.2, and wherein the trough is defined by the wall arc having end points Tm.
11. A method of claim 10, wherein the method of shaping comprises a shaping operation selected from the group consisting of injection molding, extrusion, and blow molding.
12. A method for absorbing shocks in an automobile suspension comprising using a jounce bumper to absorb energy from displacement of the suspension, wherein the jounce bumper is made of elastomeric thermoplastic material and comprises a hollow elongated tubular body having a wall, the tubular body having at least two bellows, each bellow being defined by a peak and a trough, the peak having a fillet radius of rs, the trough having a fillet radius of rc and a maximum wall thickness at the trough of Tmax; wherein rc is greater than rs, and wherein the ratio of Tmax the thickness of the wall at a trough, to Tm, the thickness of the wall at an intermediate point between peak and trough, is greater than or equal to 1.2.
13. A jounce bumper according to claim 1 wherein Tmax occurs substantially in the middle of the trough.
14. A method according to claim 10 wherein Tmax occurs substantially in the middle of the trough.