*Challenge question #52 (05/06/2017)*

**Junior Question**

$4$ large circles are placed around a small circle so that each of the circles touch as shown.

If the small circle has radius $1$ cm, what is the radius of the large circles?

**Hint**:

If two circles touch, the line joining their centres passes through their point of contact.

**Senior Question**

There is only one three-digit number $ABC$ whose value is equal to the sum of the factorials of its digits $A!+B!+C!$ . Can you find it?

**Hint**: $A$, $B$, and $C$ are distinct digits.