Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Magazines

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Jack of Cards

Stage: 2 and 3 Short Challenge Level:

Suppose the cards started as A, B, C, D and E in that order. Jack then hands over A, puts B on the bottom, hands over C, puts D on the bottom and hands over E. The cards are then in the order BD, so B is placed on the bottom and D is handed over.

This means I receive the cards in the order A, C, E, D, B. This is in order, so A is the Ace, C the 2, E the 3, D the 4 and B the 5. Hence, the original order was Ace, 5, 2, 4, 3.

This problem is taken from the UKMT Mathematical Challenges.
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