### BULLET BRAIN BUSTER

#### Pink Pink Pink Pink

PINK x 4 = KNIP

Each instance of a letter stands for the same digit, no two letters represent the same digit, and P cannot be 0. Which digits do the four letters represent? ###### More Caffeine Bullet Brain Busters

Since the product is four digits long, PINK can be no greater than 9999/4. Thus the largest PINK can be 2499. This tells us that P is either 1 or 2.

Can P be 1? We also know that K x 4 ends in P. Since 4 is even and an even number times anything results in an even number, P must be even. Thus P can’t be 1, so must be 2.

2INK x 4 = KNI2

Since P = 2, we know 2INK is somewhere between 2000 and 2499. Thus the product is somewhere between 8000 and 9996, and K must be 8 or 9.

Can K be 9? We know that K x 4 results in a number that ends in 2. 9 x 4 = 36, which ends in 6. 8 x 4 = 32, which does end in 2. Thus K = 8.

2IN8 x 4 = 8NI2

When we multiply 8 by 4, we get 32. We write down the 2 and carry the 3. Thus we know that N x 4 + 3 ends in I. Since N x 4 is even, N x 4 + 3 must be odd, so I is odd. Since the product is between 8002 and 8992, 2IN8 must be between 2001 and 2248.  So I is between 0 and 2.  The only odd number in that range is 1, so I = 1.

21N8 x 4 = 8N12

For N x 4 + 3 to end in 1, N x 4 must end in 8. The only values that will work are 2 and 7. P is already 2, so N can’t be 2. Thus N must be 7. Checking our work, we indeed get that

2178 x 4 = 8712

So we see that 2178 times 4 equals its reverse. Furthermore, 2178 x 2 = 4356 and 2178 x 3 = 6534, and those values are the reverse of each other as well.