# Bogglers Solutions

Friday, December 03, 2004

RECOMBINANT WORDS

1. DNA, and

2. none, neon

3. reef, free

4. unable, nebula

5. brainy, binary

6. dilate, detail

7. algorithm, logarithm

8. triangle, altering

9. calibrate, bacterial

10. prenatal, paternal, parental

1. DRY ICE AGE

2. PERPETUAL MOTION SICKNESS

3. STROBE LIGHT WAVE

4. CLEAN ROOM TEMPERATURE

5. BINARY STAR FISH

6. FUEL CELL DIVISION

7. FOOD CHAIN REACTION

8. COMMON COLD FUSION

ENTANGLED LETTERS

1. From each of the two Rs there are eight ways to spell RACE, for a total of 16 (eight from each of the two Rs).

2. It helps to split the word into two parts and to note that RACECAR is a palindrome—a word that reads the same forward or backward. To spell RACECAR, you must go from an R to an E and then from an E to an R. There are two paths from each R to each corner E and two paths from each corner E to each corner R. So starting at the bottom right R and going through the two corner Es, there are four paths (2 x 2). There are also four paths starting at the top left R and going through the corner Es, for a total of eight paths through the corners. There are six paths from the two Rs to each middle E. Starting from each middle E, the same sixth paths also get you from the E to an R. So the total number of full paths through each middle E is 36, or 6 x 6. The total number of ways to spell RACECAR is therefore 80 (8 + 36 + 36).

3. The answer is larger than the answer to the previous problem. Each path that spells ECARACE goes from an E to an R and then from the R to an E. From each R there are eight different paths to an E. The same paths also lead from an E to the same R. So there are 64 (8 x 8) ways to spell ECARACE for each of the two corner Rs, for a total of 128 ways.