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Answer for the clue ""And we'll ___ a cup o' kindness yet": Burns ", 3 letters:
tak

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In computer science , the Tak function is a recursive function , named after Ikuo Takeuchi (竹内郁雄). It is defined as follows: $\tau (x,y,z) = \begin{cases} \tau (\tau (x-1,y,z) ,\tau (y-1,z,x) ,\tau (z-1,x,y) ) & \text{if } y < x \\ z & \text{otherwise} ...