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Sunday Afternoon Maths IL

 Posted on 2015-12-06 

Santa

Each of the letters D, A, Y, S, N, T, B, R and E represents a different non-zero digit. The following sum is true:
$$ \begin{array}{cccccc} D&A&D&D&Y\\ B&E&A&R&D&+\\ \hline S&A&N&T&A \end{array} $$
This has a unique solution, but I haven't found a way to find the solution without brute force. This less insightful sum is also true with the same values of the letters (and should allow you to find the values of the letters using logic alone):
$$ \begin{array}{ccccc} R&A&T&S\\ N&E&R&D&+\\ \hline S&A&N&E \end{array} $$

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Shooting hoops

Source: Alex Bolton
You spend an afternoon practising throwing a basketball through a hoop.
One hour into the afternoon, you have scored less than 75% of your shots. At the end of the afternoon, you have score more than 75% of your shots.
Is there a point in the afternoon when you had scored exactly 75% of your shots?

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The self referential crossword

Fill in the following crossnumber grid so that each clue describes the solution.
For example, if some clues read "TEN DS", "ONE X" and "THREE ES" then there will be ten Ds, one X and three Es in the completed grid. The entries in the crossword include the spaces.
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about perfect numbers, or a random puzzle.

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