# What is a Flawless Word™?

This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

An entry into the 20th fortnightly topic challenge.

# Main puzzle: If a word conforms to a certain rule, I call it a Flawless Word™. Use the following examples to find the rule:

Here is a CSV:

Flawless Words™,Non-Flawless Words™
DOG,CAT
EFFACE,APPEAR
HIDE,SEEK
MAGE,FIRE
BEAR,WOLF
DEICE,WATER
GAME,WORK
HEAL,HARM
TEA,PEA
ALGAE,OCEAN


The puzzle relies on the series' inbuilt assumption, that each word can be tested for whether it is a Flawless Word™ on its own.

These are not the only examples of Flawless Word™ (or non-Flawless Word™), more can be found.

A Flawless Word™ is a word that

its letters add up to 26.

Take the first word:

3 +1 +4 +4 +9 +5 = 26.

The second:

DOG

4 + 15 +7 = 26

EFFACE

5 + 6 +6 +1 +3 +5 = 26

They are probably called 'Flawless' because that's

the number of letters in the alphabet.

• HOW DO YOU GET THESE SO FAST – greenturtle3141 Nov 27 '16 at 8:16
• @greenturtle3141 I always try those an these TM puzzles. – Mithical Nov 27 '16 at 8:17
• @Mithrandir - Wow! How is my answer works here as well :D +1 for you anyway. Not sure which one is the ONE! – Techidiot Nov 27 '16 at 8:22
• @Mithrandir PEE is my mistake... I am gonna update it... – Oray Nov 27 '16 at 9:05
• @Techidiot In your answer, you use (27-n) instead of n for the nth letter, so for a word with k letters, you'll get sum 27k-S where this answer gets S. And S=26 implies that modulo 9, we have 27k-S = -26 = 1 (mod 9), which is why your pattern works. But not the other way around: you can get sums (27k-S) that are 1 mod 9 without S being exactly 26: it can be any number that is 8 mod 9 (such as 8, 17, 26, 35, 44,...). – ShreevatsaR Nov 28 '16 at 6:52

The Flawless words are those -

Which when summed to one digit gives answer as "1". Where alphabets are assigned values from A=26, B=25...

Examples -

CADDIE = 24 + 26 + 23 + 23 + 18 + 22 = 136 = 1+3+6 = 10 = 1+0 = 1
DOG = 23 + 12 + 20 = 55 = 5+5 = 10 = 1+0 = 1
EFFACE = 22 + 21 + 21 + 26 + 24 + 22 = 136 = 1+3+6= 10 = 1+0 = 1
HIDE = 19 + 18 + 23 + 22 = 82 = 8 + 2 = 10 = 1+0 = 1

Non-Flawless words do not follow this property

GOLFER = 20 + 12 + 15 + 21 + 22 + 9 = 99 = 9+9 = 18 = 1+8 = 9
CAT = 24 + 26 + 7 = 57 = 7+5=12 = 1+2 = 3
APPEAR = 26 + 11 + 11 + 22 + 26 + 9 = 105 = 1+0+5 = 6
SEEK = 8 + 22 + 22 + 16 = 68 = 6+8 = 14 = 1+5 = 6
FIRE = 21 + 18 + 9 + 22 = 70 = 7+0 = 7

These may be called Flawless because,

flawless is a synonym of entire and word ENTIRE follows the same rule. Other reason could be, number 1 is considered as PERFECT and perfect is nothing but Flawless.

• PEE is my mistake... I am gonna update it... – Oray Nov 27 '16 at 9:05
• @Oray- Great then! Also accept the answer which was on your mind considering that the question has two solutions now. – Techidiot Nov 27 '16 at 9:06