Math-related puzzles

(1) Prove or disprove:

The product of any pair of twin primes, when increased by 1, always gives a perfect square.

(2) Prove or disprove:

π log γ = γ log π [I mean this γ]

(3) Prove or disprove:

1 + 2 = 3
1*2 + 2*3 + 3*4 = 4*5
1*2*3 + 2*3*4 + 3*4*5 + 4*5*6 = 5*6*7
etc.

(4) 2 2 2 3 2 2 4 2 3 ?

(5) Compute 1/49 to 12 digits, in your head.

(6) Name two famous mathematicians whose names are synonymous.


Bonus true story:

Grading papers in a graph-theory course. Problem: prove that if G is not connected, then the complement of G is connected.

"We use a contrapositive proof..."


© 1985-2011, S.E.

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