# Questions tagged [blackboard]

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

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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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### 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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### 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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### 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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### 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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### 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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