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The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word.

Table:

Proof:

XEROX (1 X in Scrabble, 1 blank tile);
FLUFFY (2 Fs in Scrabble, 1 blank tile);
JUJITSU (1 J in Scrabble, 1 blank tile);
BUBBLES (2 Bs in Scrabble, 1 blank tile);
ECLECTIC (2 Cs in Scrabble, 1 blank tile);
PINEAPPLE (2 Ps in Scrabble, 1 blank tile);
CHIHUAHUA (2 Hs in Scrabble, 1 blank tile);
CLOCKWORK (1 K in Scrabble, 1 blank tile);
COMMUNISM (2 Ms in Scrabble, 1 blank tile).

Words which are not Bedspread Words™

can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...

Therefore, two blank (bedspread) tiles are needed.

The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word. If you lookup "Bedspread" in a thesaurus, you will find the word "Blanket", which makes sense in this case.

Table:

Proof:

XEROX (1 X in Scrabble, 1 blank tile);
FLUFFY (2 Fs in Scrabble, 1 blank tile);
JUJITSU (1 J in Scrabble, 1 blank tile);
BUBBLES (2 Bs in Scrabble, 1 blank tile);
ECLECTIC (2 Cs in Scrabble, 1 blank tile);
PINEAPPLE (2 Ps in Scrabble, 1 blank tile);
CHIHUAHUA (2 Hs in Scrabble, 1 blank tile);
CLOCKWORK (1 K in Scrabble, 1 blank tile);
COMMUNISM (2 Ms in Scrabble, 1 blank tile).

Words which are not Bedspread Words™

can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...

Therefore, two blank (bedspread) tiles are needed.

The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word.

Graph:

Proof:

 BUBBLES (2 Bs in Scrabble, 1 blank tile).

Not Bedspread Words™ can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...
Therefore, two blank (bedspread) tiles are needed).

The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word.

Table:

Proof:

XEROX (1 X in Scrabble, 1 blank tile);
FLUFFY (2 Fs in Scrabble, 1 blank tile);
JUJITSU (1 J in Scrabble, 1 blank tile);
BUBBLES (2 Bs in Scrabble, 1 blank tile);
ECLECTIC (2 Cs in Scrabble, 1 blank tile);
PINEAPPLE (2 Ps in Scrabble, 1 blank tile);
CHIHUAHUA (2 Hs in Scrabble, 1 blank tile);
CLOCKWORK (1 K in Scrabble, 1 blank tile);
COMMUNISM (2 Ms in Scrabble, 1 blank tile).

Words which are not Bedspread Words™

can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...
 
Therefore, two blank (bedspread) tiles are needed.

The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word.

Graph:

Proof:

Not Bedspread Words™ can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...
Therefore, two blank (bedspread) tiles are needed).

The following words are Bedspread Words™ because:

Using the standard number of tiles in a Scrabble set, a blank tile will be needed to write out the word.

Graph:

Proof:

BUBBLES (2 Bs in Scrabble, 1 blank tile).

Not Bedspread Words™ can be made with the standard Scrabble letter count.

ZIGZAGGING is a Double Bedspread Word™ because:

ZIGZAGGING (3 Gs and 1 Z in Scrabble, 1 blank tile for G, 1 blank tile for Z)...
Therefore, two blank (bedspread) tiles are needed).