How many squares, of any size, can be found on a standard chessboard? How many rectangles, of any size, can be found on a standard chessboard?
Remember when counting the rectangles, that squares are also rectangles.
Hint
How many 8x8 squares are there, what about 7x7.
Answers 204 squares.1,296 rectangles, which also includes the squares.
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Puzzle 2
Take a word from the first column, and a word from the second column.
You will now have 6 lots of eight letters, and each of these eight letters is an anagram of something that lives in water.
dish leek
tray shoe
raft sign
cram golf
ears fern
loud hiss
Hint
What must the middle temperature be? Remember that the temperature are in degrees Celsius.
Answer
The temperatures were -6, -2, 2, 6, 10 °C.
Each day increased by a steady 4 degrees.
Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).
Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).
If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.
If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does matches all of the requirements.
If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.
Any larger increase makes the product even larger, so we can stop checking.
So the only possible answer is -6, -2, 2, 6, 10.
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Puzzle 4
Can you find every occurrence of the word LOVE that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
