Recently posted problems (14 days):
Show Digest for last:
2 Days 
3 Days 
5 Days 
1 Week 
2 Weeks
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 a_{i} to Erdös, who then chooses a non negative integer b_{i}, and then Oleg defines a_{i+1} = a_{i}b_{i} or a_{i+1} = a_{i} + b_{i}. Erdös wins if a_{20} is a power of 10, otherwise Oleg wins.
Who is the winner, Oleg or Erdös?
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 (M1) 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.
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?
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.
5 dice
(in Probability)
Rating: 3.00
Andy rolls five regular dice. What is more likely: rolling no sixes or rolling exactly one six?
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 nonoverlapping circles placed inside it?
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.
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?
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.
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.
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?
Find all primes p such that 11+p^2 has exactly six different positive divisors (the number itself included).
LOVE*IS=BLIND has 2 solutions, one of them using a zeroless set.
Find both.
2 & 5 =14
3 & 1= 23
100 & 8= 25 100 & 100= 27
16 & 6 =33
17 & 11= 46
7 & 11 = ?
