Extra Practice & Challenges

Challenge 1: The Lychrel Number

We learned that 196 might never become a palindrome. Try the Reverse-and-Add process on 196 for 5 steps.

1. $196 + 691 = 887$
2. $887 + 788 = 1675$
3. $1675 + 5761 = 7436$
4. $7436 + 6347 = 13783$
5. $13783 + 38731 = 52514$ Does it look like it’s getting closer? The numbers just get bigger!

Challenge 2: Supercell Grid Design

Design a $3 \times 3$ grid using numbers 1 to 9 (used once each) such that there are 5 supercells. Is it possible?

• To be a supercell, a number must be larger than neighbors.
• Checkerboard pattern: Corners (4) + Center (1) = 5 cells.
• Place $9, 8, 7, 6, 5$ in the “Super” positions (Corners and Center).
• Place $1, 2, 3, 4$ in the “Edge” positions.
• Check: Center (5) must be larger than Edge neighbors (1,2,3,4). Yes!
• Corners (9,8,7,6) are definitely larger than neighbors (1,2,3,4).

Solution Grid:

(Verify: 5 is > 1,2,3,4? Yes. 9 > 1,2? Yes. etc.)

Challenge 3: Mental Math

Calculate $999 \times 6$ without standard multiplication. Strategy: $999 = 1000 - 1$ $(1000 - 1) \times 6 = 6000 - 6 = 5994$

Try: $34 \times 11$. Strategy: Split the 3 and 4, sum them (7), place in middle. $374$