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
...
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votes
1
answer
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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 ...
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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 ...
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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!
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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 ...
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votes
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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 ...
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2
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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,...
- 2,346
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votes
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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 $[B]$ ...
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11
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3
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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 ...
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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 $ ...
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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 $ ...
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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 ...
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votes
2
answers
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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 ...
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votes
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The smallest value 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....
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Numbers on the blackboard: From 2-2015 to 1-2014
The numbers $ 2, \ldots, 2015 $ are written on a blackboard. Each minute any two numbers $ x $ and $ y $
are wiped out and are replaced by two numbers $\displaystyle \frac { 4x + 3y } { 5 } $ and $...
- 11.7k
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votes
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Triangle of numbers on a blackboard
Ten rows of numbers are written on a blackboard. The first row has one $1$, the second has two $2$'s, and so on up through the tenth row with ten $10$'s:
$$
\begin{gather*}
1\\
2,\;2\\
3,\;3,\;3\\
\...
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The last number on the blackboard
The numbers 1, 2, ..., 500 are written on a blackboard. Each minute any two numbers
are wiped out and their positive difference is written instead. At the end only one number remains.
Which values can ...
- 11.7k
8
votes
2
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Numbers on a Blackboard
You are given an empty blackboard. Once a minute, you are allowed to do one of the following:
Write two $1$'s on the blackboard
Erase two copies of a number, $n$, and replace them with $n-1$ and $n+...
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Ten numbers on a blackboard
The numbers 1 through 10 are written on a blackboard. You erase two numbers of your choice, and write their product plus their sum
$$a,b \to ab+a+b$$
So, now there are nine numbers on the board. You ...
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