Time Tables in Disguise

We can form a new puzzle by disguising a times table. Take a times table and to each pile add the same number.

For example take the four times table

and add a Three card to each pile.

Calculating the resulting numbers give this sequence of cards

We have taken a hand in the four times table and

added three to the hand .

This is recorded as 4x + 3, with the result depending on the declared value for x.

As it is based on the four times table we note that each number in the sequence is four more than the previous number.

This leads to two new puzzles.

1.  Given a sequence of numbers find out if it is a disguised times table and find the hand that would play the sequence.
2. From a maths record of a disguised times table find the declared value of x.

These will be described in the next two blogs.