Logic: Self-Referential Puzzles

Hints [solutions at the bottom]

My First One – a Self-Counting Sentence

As you fill in blanks you will have to back up and re-adjust the counts. Some of these have no solution which causes you to go in endless circles of re-adjustment. This puzzle has two solutions.

Angels and Devils

Think "big picture." Each statement contradicts all the others. Can there be a true statement at all?

Cross Number Puzzle

Fill in the "uninvolved" answers like 9 Across. Then look for clues that involve those answers. You may need to make some inferences about parts of answers, like final or initial digits, and then revisit those clues later.

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Nothing in Common

# 1-16 in order are neigh, scour, light, score, night, close, right, clues, thing, rouse, cling, south, reign, shout, cline, torus.

Other solutions possible. Send us yours!

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Department of Words


From left to right find BUCKET.

From right to left find STRONG.

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Five and Ten

Puzzle 1. Silverback   Puzzle 2. Battleship

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Fit for Four

1. chief    2. wide    3. major    4. pocket

5. stage   6. drive    7. here    8. hands

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Crisscross Crunch

Across, in row order: driver, verify, yes; dye, yeti, tightwad; copper, Erie, eggy; snide, defame, amend; total, talent, entice.

Down, in column order: Greyhound, undo, doe; e-vite, tepid, ideal; brig, Igor, rifles; UFO, other, Hermits; Cesar, argon, neck.

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Across 1. Torpedo (toro + ped)    4. Timed (ti + med)    6. Xenon (X + none, rev.)
7. Arbiter (ar + biter)

Down 1. Titania (titan + IA)    2. REMAX (re + max)    3. O'Connor (Sandy Day, sp.)
5. Donut (don + UT)

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Logic: Self-Referential Puzzles

“In this sentence the number of occurrences of e is __ELEVEN___.”

My First One – a Self-Counting Sentence

“In this sentence, the number of occurrences of 0 is __1__, the number of 1s is _7___,

the number of 2s is __3__, of 3s is _2___, of 4s is __1__, of 5s is __1__, of 6s is _1___, of 7s is

__2__, of 8s is __1__, and the number of 9s is __1__.”

Solving involves what might be termed false position. At times you are forced to fill in a digit you know to be wrong, but repeated adjustment allows the dust to settle into a perfect solution – when there is one.

In your trials you may have come upon a second solution. See it here:

For an in depth look at this type of puzzle see

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Angels and Devils

Person 9 is the sole Angel in the group. Person 10's statement must be false because it cannot be both true and false. So there is at least one Angel. Because all statements disagree, there can be at most one Angel.

Cross Number Puzzle

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