# Questions tagged [blackboard]

In a 'blackboard puzzle' a set of numbers is transformed according to certain rules.

15 questions
Filter by
Sorted by
Tagged with
81 views

### Puzzle on a blackboard [closed]

What is the missing number in the picture above?(question is from some puzzle game) I tried some approaches, but haven't found any meaningful rule..thanks in advance!
243 views

### Positive integers on a blackboard

Consider a blackboard with some positive integers written on it. A move consists one of the following actions: Choose two integers $m$ and $n$ on the board, remove them, and write $m+n$ on the ...
116 views

### Aatif averages numbers on the blackboard

Aatif has averaged numbers and made the final number $2$: Averaging numbers on the blackboard Today Aatif once again sees the numbers $1 , 2 , 3 , .... , 2016$ written on the blackboard. In one ...
2k views

### Averaging numbers on the blackboard

Aatif sees the numbers $1 , 2 , 3 , .... , 2016$ written on the blackboard. In a move Aatif can pick any two numbers on the blackboard, erase them and write instead once their average. As an example,...
333 views

### Make a certain number with an unusual calculator

The Kasio Kool-Kalk™ is a poorly-designed calculator with only two buttons, labelled $[A]$ and $[B]$. Pushing $[A]$ replaces the currently displayed number $x$ with $2-\frac{1}{x}$. Pushing $[B]$ ...
334 views

### Blackboard problem with polynomial

At the beginning the blackboard contains $n$ real numbers, one of which is $0$. In every step, we may take any polynomial such that all its coefficients are currently on the blackboard, we compute all ...
298 views

### Blackboard problem with 2016

At the beginning the blackboard contains a single integer $N$. If the blackboard contains some number $x$, then we may additionally write the two numbers $\displaystyle\frac x {x+2}$ and $2x + 1$ ...
518 views

### Blackboard problem with polynomial

The blackboard contains the two numbers 0 and 120. Each minute you are allowed to write an additional number $x$ on the blackboard if $x$ has not been written before on the blackboard and if $x$ ...
2k views

### Blackboard cleaning

The blackboard contains 30 integer numbers from 1..2000. Each minute you are allowed to elect some positive integer number x and subtract x from some (chosen by you) of the numbers on the blackboard ...
The square numbers $1^2, 2^2, 3^2, 4^2, \cdots, 100^2, 101^2$ are written on the blackboard. Each minute any two numbers are wiped out, and the absolute value of their difference is written instead....