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.

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?

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?

Remainders

Age 7 to 14Challenge Level

I'm thinking of a number.
My number is both a multiple of $5$ and a multiple of $6$.
What could my number be?
What else could it be?
What is the smallest number it could be?

I'm thinking of a number.
My number is a multiple of $4$, $5$ and $6$.
What could my number be?
What else could it be?
What is the smallest number it could be?

The Number Sieve below can be used to explore questions like the ones above and many more.  Why not experiment and see what you can discover?

Here are some more questions you might like to consider:

I'm thinking of a number that is $1$ more than a multiple of $7$.
My friend is thinking of a number that is $1$ more than a multiple of $4$.
Could we be thinking of the same number?

I'm thinking of a number that is $3$ more than a multiple of $5$.
My friend is thinking of a number that is $8$ more than a multiple of $10$.
Could we be thinking of the same number?

I'm thinking of a number that is $3$ more than a multiple of $6$.
My friend is thinking of a number that is $2$ more than a multiple of $4$.
Could we be thinking of the same number?

Here's a challenging extension:

We know that

When 59 is divided by 5, the remainder is 4
When 59 is divided by 4, the remainder is 3
When 59 is divided by 3, the remainder is 2
When 59 is divided by 2, the remainder is 1

Can you find a number with the property that when it is divided by each of the numbers 2 to 10, the remainder is always one less than the number it is has been divided by?
Can you find the smallest number that satisfies this condition?

If you haven't already explored The Remainders Game, why not take a look now?