# Questions tagged [blackboard]

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

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### Variant of Abby and Bob and 3 numbers on the blackboard

Abby selects a positive integer $A$, and Bobby selects a positive integer $B$. They then both tell their number secretly to Summy. Summy writes the numbers $5$, $8$, and $15$ on the blackboard, and ...
151 views

### Replacing numbers on a board by their difference [duplicate]

The numbers from 1 to 1000 are written on a board. You are allowed to select any two numbers, erase them and write their difference on the board. If this process is repeated often enough, there is ...
541 views

### 99 numbers on the blackboard

The numbers 1,2,3, ..., 99 are written on the blackboard. Alice and Bob play the following game, taking turns. Alice starts. At every turn, each player removes one number until two numbers are ...
288 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!
391 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 ...
140 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,...
370 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 $[B]$ ...
388 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 ...
320 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 $2x + 1$ ...
587 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 $x$ ...
3k views

### Abby and Bobby and three numbers on the blackboard

Abby selects a non-negative integer $A$, and Bobby selects a non-negative integer $B$. They then both tell their number secretly to Summy. Summy writes the numbers $5$, $8$, and $15$ on the ...
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....