A word ladder (also known as doublets) is a word game invented by Lewis Carroll.   A word ladder puzzle begins with two words, and to solve the puzzle one must find a chain of other words to link the two, in which two adjacent words differ by one letter.   Here is an example:

Change TEN to SIX.
T E N
T I N
S I N
S I X

Here are four math doublets proposed by Roger Robison.   You must solve three of them to get credit for this month's problem.

Change ZERO to NULL

Change ONE to TWO

Change FOUR to FIVE

Change TAN to ARC
Solution to the Problem:

Change ZERO to NULL

Z E R O
H E R O
H E L O
H E L L
H U L L
N U L L

Z E R O
H E R O
H E R E
H A R E
H A R T
H U R T
H U R L
H U L L
N U L L
Zero/Hero/Herd/Held/Hell/Fell/Full/Null



Change ONE to TWO

O N E
O D E
O D D
A D D
A I D
B I D
B A D
C A D
C O D
C O O
T O O
T W O

one/ore/ort/out/tut/tot/too/two


Change FOUR to FIVE

F O U R
F O U L
F O I L
F A I L
F A L L
F I L L
F I L E
F I V E

four/tour/tout/toot/tool/toll/till/tile/file/five

F O U R
D O U R
D O U T (To put out)
P O U T
P O S T
P O S E
P O L E
P A L E
P A V E
G A V E
G I V E
F I V E
Four/Foul/Fool/Food/Fond/Find/Fine/Five



Change TAN to ARC

T A N
P A N
P I N
D I N
D I M
A I M
A R M
A R C

tan/can/cat/cut/out/ort/art/arc

Tan/Ran/Ram/Ham/Him/Aim/Arm/Arc

Correctly solved by:

1. Roger Robison   *** San Antonio, Texas
2. Ivy Joseph Pune, Maharashtra, India
3. SreeRoopa Sankararaman *** Singapore, Singapore
4. Frankie Jenkins Mountain View High School,
Mountain View, Wyoming
5. Brijesh Dave *** Mumbai City, Maharashtra, India
6. Kaylee Gross Mountain View High School,
Mountain View, Wyoming
7. Hunter Gross Mountain View High School,
Mountain View, Wyoming
8. Mairany Jaracuaro Delta High School,
Delta, Colorado
9. Alyssa Marke   *** Delta High School,
Delta, Colorado

        *** solved the extra credit