### Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.

### Double Time

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

# Function Pyramids

##### Stage: 5 Challenge Level:

This problem explores structures like those found in Number Pyramids and More Number Pyramids.

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it, together with some function:

The function used in the problems Number Pyramids and More Number Pyramids could be expressed as:
$$f(a,b) = a+b$$

Here is a function pyramid for you to explore. Type some numbers into the three spaces on the bottom layer.

Can you figure out how the rest of the pyramid is generated?

Here are some questions you might like to consider:

Can you choose numbers for the bottom layer so that the number 1 appears in the top cell?
Can you choose numbers for the bottom layer so that the number 5 appears in the top cell?
Can you identify the function used to determine the next layer, given the bottom layer?
Can you choose numbers for the bottom layer so that the number in the top cell is negative?

Why not make up some function pyramids of your own, and ask yourself some similar questions?