** Can you explain what is going on in these puzzling number tricks?**

*You may wish to look at Always a Multiple and Reversals before tackling this problem.*

**For these problems, use the digits from 1 to 9**

We are using ABC to represent a 3 digit number with A hundreds, B tens and C units. Similarly, AB represents a 2 digit number with A tens and B units.

**Problem 1:**

Prove that there are exactly four such numbers AB.

**Problem 2:**

**Problem 3:**

**different**digits (e.g. 47) and form its reversal (i.e. 74). Now, subtract the sum of the digits from each of these numbers, and then add the two results. Show that you always obtain a multiple of 9.

**Problem 4:**

Choose three different digits and form the six two-digit numbers that use two of the three digits. Add these six possibilities and divide this total by the sum of the three digits. Show that you always obtain 22.

**Problem 5:**

Work out the differences between the two-digit numbers you can make and their reverses (e.g. 86−68;63−36;83−38), then add these three results.

Show that you always obtain a multiple of 18.

**Problem 6:**

**Problem 7:**

without any of the four digits being the same (e.g. 97+24=42+79).

What general rule must apply? Why?

Age 14 to 16