This week's Problem is in honor of our newest grandchildren who were born this summer -- Kate
Cotter and Jackson Harding.
Given the set of letters below, you are to spell the
names KATE and JACKSON by starting at the top of the
rhombus and moving down through the letters. At each
level, you must move to a letter which is below and
to the immediate left, or below and to the immediate
right, of the letter you are at. In how many ways can
you spell out the names KATE and JACKSON by moving from the
top letter and ending at the bottom letter?
K
A
A
T
T
T
E
E
E
E
J
J
J
J
J
A
A
A
A
A
A
C
C
C
C
C
K
K
K
K
S
S
S
O
O
N
| K | ||||||||||
| A | A | |||||||||
| T | T | T | ||||||||
| E | E | E | E | |||||||
| J | J | J | J | J | ||||||
| A | A | A | A | A | A | |||||
| C | C | C | C | C | ||||||
| K | K | K | K | |||||||
| S | S | S | ||||||||
| O | O | |||||||||
| N |
Solution to the Problem:
There are 252 different ways to spell the names. You could use "Pascal's Triangle" to help solve it. I have replaced the letters of KATE and JACKSON by numbers representing how many different ways you could reach that particular letter.
I also accepted separate answers for each: there are 8 ways to spell Kate and 62 ways to spell Jackson (using Pascal's Triangle).
| 1 | ||||||||||
| 1 | 1 | |||||||||
| 1 | 2 | 1 | ||||||||
| 1 | 3 | 3 | 1 | |||||||
| 1 | 4 | 6 | 4 | 1 | ||||||
| 1 | 5 | 10 | 10 | 5 | 1 | |||||
| 6 | 15 | 20 | 15 | 6 | ||||||
| 21 | 35 | 35 | 21 | |||||||
| 56 | 70 | 56 | ||||||||
| 126 | 126 | |||||||||
| 252 |
Correctly solved by:
| 1. Keith Mealy * | Cincinnati, Ohio |
| 2. Richard Johnson | LaJolla, California |
| 3. James Alarie | University of Michigan -- Flint, Flint, Michigan |
| 4. Jeffrey Gaither | Winchester, Virginia |
| 5. David & Judy Dixon | Bennettsville, South Carolina |
| 6. David Amos | Winchester, Virginia |
| 7. Larry Schwartz | Trumbull, Connecticut |