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Questions tagged [blackboard]

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

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20 votes
2 answers
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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 ...
Haobin's user avatar
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47 votes
2 answers
5k views

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 ...
xnor's user avatar
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16 votes
6 answers
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 ...
Gamow's user avatar
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13 votes
2 answers
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,...
D.A.G.'s user avatar
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