# Bogglers Solutions

By Scott Kim|Friday, March 01, 2002

NUMEROUS ANALOGIES

1a. (1 1 2) (1 1 2 3) (1 1 2 3 4) ... — lengthening sequences
1b. (1) (1 2 1) (1 2 3 2 1) (1 2 3... — lengthening mountains
1c. (1 1 2) (1 1 2) (1 1 2) (1 1 2)... — simple repetition

2a. (1) (0 0) (1 1 1) (0 0 0 0) (1 1 1... — lengthening repetitions
2b. 1 0) 0 (1 1 1) 0 (2 1 2) 0 (3 1... — x1x with 0's inbetween
2c. (1 0 0) (1 1 1) (1 2 2) (1 3 3) (1... — 1xx with increasing x

3a. (2 1) (2 2) (2 3) (2 4) (2 5) (2 6) (2... — 2x with increasing x
3b. (2) 1 (2 2 2) 3 (2) 5 (2 2 2) 7 (2)... — odd numbers alternate with (2) and (2 2 2)
3c. (2 1 2 2) (2 3 2 2) (2 5 2 2) (2... — 2x22 with increasing odd x

4a. (1 1 2) (1 2 3) (1 3 4) (1 4 5) (1... — 1x[x+1] with increasing x
4b. (1) (1 2) (1 2 3) (1 2 3 4) (1 2 3... — lengthening sequences
4c. 1 1 2 1 2 3 3 3 3 5 4 5 4... — two interleaved increasing sequences

5a. (1 1 2) (3 3 5) (5 5 8) (7 7 11) (9 9 14)... — xx[x+y] with increasing x, y
5b. 1 1 2 3 3 5 4 7 5 9 6 11 7 13 8... — two interleaved increasing sequences
5c. (1 1) (2 3 3) (5 7 7 7) (10 13 13 13 13) (17... — lengthening x[x+y]

6a. (2 1) (1 2 1) (2 1 2 1) (1 2 1 2 1) (2 1 2 1 2) (1... — lengthening oscillating sequences between 1 and 2, where the first number of each sequence alternates between 2 and 1.
6b. 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2... — 2's separated by one or two 1's, where the number of 1's in each group is itself the same sequence 2 1 1 2 1 2...
6c. (2 1 1) (2 1 2) (1 2 1) (1 2 2) (2 1 1) (2 1 2) (1 2 1) (1 2 2)... — repeating sequence of the form ABC, where A and B alternate slowly between 1 and 2, and C alternates quickly between 1 and 2.

Type design is a subjective art, so don't be alarmed if your answers are not exactly the same as those shown here.

1. Standard Square, minus upper left horizontal segment

2. Spiral, with ends that stop one short

3. House shape

4. Hexagon shape pointing up to right

5. Double down-sloping diagonal

6. The shape of a half-opened staple

7. All diagonal lines

LETTERS ARE TO LOGIC AS ABC IS TO . . . ?

These are not the only possible interpretations of the following letter-based analogy problems. 1. AABC is to AABD as IJKK is to . . .
. . . IJLL advances the final letter, the repeated K.
. . . HJKK replaces I with the preceding letter H, reversing the initial string's pattern and recognizing that the repeated letter is at the opposite end of the string from the "advanced" letter.

2. MNO is to MNP as MRRJJJ is to . . .
. . . MRRKKK advances the final letter, which is in this case the repeated J.
. . . MRRJJJJ recognizes that the sequence is no longer alphabetical, so instead of tracking the alphabetical position, it picks up on the number of repetitions of each letter in MRRJJJ, to produce the sequence 1 2 3. Advancing the last term in this sequence creates the sequence 1 2 4, which translates back into MRRJJJJ.

3. EFG is to DFG as GHI is to . . .
. . . FHI takes the predecessor of the first letter.
. . . GHJ recognizes that EFG and GHI are mirror-image sequences, growing to the left and right of the central letter G. Therefore, changing the first letter E into the letter D "reflects" into changing the last letter I into the letter J.

4. EQE is to QEQ as RVVVR is to . . .
. . . VRRRV reverses letters.
. . . RRRVRRR reverses the number of repetitions.

5. FG is to GH as FFG is to . . .
. . . GGH advances each letter.
. . . FGFGH groups FFG as (F)(FG) and advances the length of each string.
. . . FFFGG groups FFG as (FF)(G) and adds one to the length of each string.

6. GFF is to GGF as SSSTT is to . . .
. . . SSTTT reverses the number of repetitions.
. . . TTTSS recognizes that GFF has an increasing number of repetitions, while SSSTT has an increasing alphabetical sequence and a decreasing number of repetitions. The answer TTTSS equates the increasing number of repetitions in GFF to the increasing alphabetical sequence in SSSTT.
. . . SSSSSST doubles the number of Ss and halves the number of Ts.

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