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Oleg and (the ghost of) Erdös play the following game. Oleg chooses a non- negative integer a1 with at most 1000 digits.

In Round i the following happens:
Oleg tells the number ai to Erdös, who then chooses a non negative integer bi, and then Oleg defines ai+1 = |ai-bi| or ai+1 = ai + bi.
Erdös wins if a20 is a power of 10, otherwise Oleg wins.

Who is the winner, Oleg or Erdös?

(No Solution Yet, 1 Comments) Submitted on 2017-05-26 by Ady TZIDON    

Difficulty: 3 of 5 N dice (in Probability) Rating: 3.50
In "5 dice" Andy had five regular dice. Now he has a total of N regular dice. He claims that the odds of rolling exactly M sixes is exactly half as likely as rolling (M-1) sixes. (M < N).

For what values of N is this true?

State the pattern if there is one.

Express M as a function of N.

(No Solution Yet, 3 Comments) Submitted on 2017-05-25 by Larry    

Let N(x) be the number 122....221 where the digit 2 occurs x times.

Twice in the past we have determined the highest power of 11 that divides N(2001) is 11^3.

What is the smallest x for N(x) to be a multiple of 11^3? What about multiples of 11^4 and 11^5?
(No Solution Yet, 4 Comments) Submitted on 2017-05-24 by Brian Smith    

Difficulty: 4 of 5 First or second? (in Games) Rating: 3.00
Two players alternatively erase some 9 numbers from the sequence 1,2,...,101 until only two remain. The player that starts wins x−54 dollars from the player that plays second, x being the absolute value of the difference between the remaining two numbers.

Would you rather be the first or the second player?
Explain your decision by providing your strategy.

(No Solution Yet, 5 Comments) Submitted on 2017-05-23 by Ady TZIDON    

Difficulty: 2 of 5 5 dice (in Probability) Rating: 3.00
Andy rolls five regular dice.
What is more likely: rolling no sixes or rolling exactly one six?
(No Solution Yet, 2 Comments) Submitted on 2017-05-22 by Ady TZIDON    

A 2 by X rectangle can obviously have 2*X circles of diameter 1 placed inside it without overlapping. What is the smallest integer X where a 2 by X box can have 2*X+1 non-overlapping circles placed inside it?
(No Solution Yet, 5 Comments) Submitted on 2017-05-21 by Brian Smith    

Difficulty: 3 of 5 Seven Point Placement (in Shapes) Rating: 4.00
Find a placement of a set of seven points in a plane such that if any subset of three points is chosen then at least one pair of points from the subset are unit distance apart.
(No Solution Yet, 1 Comments) Submitted on 2017-05-20 by Brian Smith    

Difficulty: 2 of 5 Four balls (in Probability) Rating: 3.50
There are four balls in a hat: a blue one, a white one, and two red ones. Now I draw simultaneously two balls, look at them, and announce that at least one of them is red.

What is the chance that the other is red as well?

(No Solution Yet, 21 Comments) Submitted on 2017-05-19 by Ady TZIDON    

Is there anything you can conclude from:

1. Everyone hates the enemy of Lady Chatterley.
2. The enemy of Lady Chatterley hates only Lady Chatterley.

(No Solution Yet, 3 Comments) Submitted on 2017-05-18 by ollie    

Difficulty: 3 of 5 Unreliable Witnesses (in Logic) Rating: 3.67
Six witnesses gave conflicting descriptions of the suspect.

Each witness had exactly one item correct. Each correct value appears at least once.

What would be the correct description of the suspect?

Hair Jacket Shirt Pants
Brown White Red Gray
Red Blue Pink White
Black Purple Yellow Blue
Blond White Not Yellow White
Brown Purple Green Gray
Gray Blue Orange Blue

This can be solved analytically without trial and error.

From Mensa Puzzle Calendar 2017 by Mark Danna and Fraser Simpson, Workman Publishing, New York. Puzzle for May 12.
(No Solution Yet, 4 Comments) Submitted on 2017-05-17 by Charlie    

Difficulty: 3 of 5 Hands off! (in Weights and Scales) Rating: 3.00
A scale balances a cup of water with a certain weight.

Will the balance be upset if you put your finger in the water, if you’re careful not to touch the glass?

(No Solution Yet, 3 Comments) Submitted on 2017-05-16 by Ady TZIDON    

Find all primes p such that 11+p^2 has exactly six different positive divisors (the number itself included).
(No Solution Yet, 1 Comments) Submitted on 2017-05-15 by Ady TZIDON    

has 2 solutions, one of them using a zeroless set.

Find both.
(No Solution Yet, 2 Comments) Submitted on 2017-05-14 by Ady TZIDON    

2 & 5 =14
3 & 1= 23
100 & 8= 25
100 & 100= 27
16 & 6 =33
17 & 11= 46

7 & 11 = ?

(No Solution Yet, 1 Comments) Submitted on 2017-05-13 by Ady TZIDON    

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