Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

[Ref: ZMNW]

Hint: There are three zeros in the number.

Answer: 3211000.

Puzzle 397

Your objective is to place some diagonal 'mirrors' into the grid.

If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.

Each row and each column will contain exactly two of the diagonal mirrors.

On the first day I travelled 60 miles, leaving 60 miles. On day two I travelled 20 miles, leaving 40 miles On day three I travelled 30 miles, leaving 10 miles. Yesterday I travelled 5 miles, leaving 5 miles. QED.

Puzzle 400

Using the BrainTracker grid below, how many words can you find? Each word must contain the central H and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?