Two fathers and two sons go fishing. Each of them catches one fish. So why do they bring home only three fish?Because the fishing group comprises a grandfather, his son, and his son's son – hence just three people.
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A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark. How many socks must he take out to make 100 per cent certain he has a pair of black socks? 40 socks. If he takes out 38 socks, although it is very unlikely, it is possible they could all be blue and red. To make 100 per cent certain that he also has a pair of black socks he must take out a further two socks;
For a 9 x 9 Sudoku puzzle with a unique solution: 1. What is the fewest possible number of shown squares with which the puzzle can be solved? 2. What is the greatest number of shown squares that can't be solved? 3. How would one determine the answers to the two questions? est 1. 17 2. 77 3. For 1, see Mathematicians Solve Minimum Sudoku Problem | MIT Technology Review . It wasn't easy. For 2, all you need are four empty squares that are the four corners of rectangle, where the rectangle goes across two boxes, and the missing numbers are two of one value and two of another. Then there are two solutions, so it can't be solved. (Note: for #2, I am assuming that you mean the puzzle can't be solved because there is more than one solution, not because there are no solutions, i.e. the puzzle is invalid. For the no solution case, the answer is arguably 81, since you can provide a filled-in puzzle that is simply wrong, and there...
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