Skip to main content
27 votes
Accepted

Averaging numbers on the blackboard

First choose $2014$ and $2016$. Average = $2015$. Now take the $2015$s. Their average is $2015$. Now choose $2015$ and $2013$. Average = $2014$. Choose $2014$ and $2012$. Average = $2013$. Note ...
iamwhoiam's user avatar
  • 1,348
19 votes
Accepted

99 numbers on the blackboard

I believe this is the answer. The strategy is below. Edit: Slightly clearer response with strategy.
cmxu's user avatar
  • 1,016
17 votes
Accepted

Make a certain number with an unusual calculator

Let $A(x)=2-\frac{1}{x}$ and $B(x)=1+\frac{1}{x-1}$. Notice: In total, the sequence of button presses is (One continued fraction representation of $\frac{1003}{100}-1$ is $[9;33,2,1]$. This is not a ...
f'''s user avatar
  • 33.7k
12 votes

Averaging numbers on the blackboard

Reasoning: After this we... ...going all the way back to...
MichaelK's user avatar
  • 709
9 votes
Accepted

Blackboard problem with polynomial

The smallest possible value of $n$ is Claim: We can get every non-negative integer $n\leq 2016$ on the board. Proof: By induction. We start with $n=0$ on the board. We can get $1$ using Lord of the ...
Julian Rosen's user avatar
  • 14.3k
7 votes
Accepted

Positive integers on a blackboard

The answer is Proof:
Ankoganit's user avatar
  • 19k
7 votes
Accepted

Aatif averages numbers on the blackboard

The answer is : Explanation : Generalization :
Fabich's user avatar
  • 7,165
6 votes
Accepted

Variant of Abby and Bob and 3 numbers on the blackboard

The first ring happens before any information is passed, so we can't draw any conclusions If the second ring happens, If the third ring happens, If the fourth ring happens,
Sconibulus's user avatar
  • 19.7k
6 votes
Accepted

Replacing numbers on a board by their difference

The answer is: The proof:
Jeremy Dover's user avatar
  • 28.4k
5 votes

Make a certain number with an unusual calculator

I wanted to post my solution as well, because it looks a little diffferent than f'''s. If we press $[A]$ repeatedly we see $\frac{3}{2}$, $\frac{4}{3}$, $\frac{5}{4}$, $\ldots$, and indeed $[A]$ ...
3 votes

Blackboard problem with polynomial

Partial Answer : (?) Explanation : Example :
Fabich's user avatar
  • 7,165
1 vote

Puzzle on a blackboard

It can be assumed that evaluation is left to right (or rather: clockwise), not by precedence rules. Then this reads and simplifies to or
Hagen von Eitzen's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible