Puzzles

Put the digits 1 to 9 (using each digit once) in the boxes so that the three digit numbers formed (reading left to right and top to bottom) have the desired properties written by their rows and columns.

Today's number is the multiple of 5 formed in the first row.

How many different triangles are there with a perimeter of 100 and each side having an integer length?

(different = not rotations or reflections)

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums reading across and down are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10.

The answer is the product of the digits in the red boxes.

In August, I wrote about MENACE, a machine learning robot built from matchboxes which plays noughts and crosses. How many matchboxes are needed to build MENACE?

In a week (Monday 12:01 to Monday 12:01 a week later), how many times will the minute hand of an analogue clock point in the same direction as the hour hand?

What is area of the largest area rectangle which will fit in a circle of radius 10?

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:

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):

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?