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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.

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Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Method in Multiplying Madness?

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

$23 \times 21$ is the same as

$$(20 \times 21) + (3 \times 21)$$

which is the same as

$$((20 \times 20) + (20 \times 1)) + ((3 \times 20) + (3 \times 1))$$

Can you figure out where each of these four products appears in the different methods?

Can you deconstruct $246 \times 34$ in the same way?