# Challenge #11 – The Library

## The Challenge

All that planning has earnt you a break, so you decide to take a nap at the library. As you make your way there, you overhear some cops discussing when the last secret bank-heist occurred in the city.

Because you’re a nosey little thief, you manage to pickpocket 2 pieces of paper from them. You need to use the 2 notes to give you the information of the date of the last bank-heist…

When was the last bank-heist?

## The Solution

### The puzzle bit

The challenge is called The Library and upon closer inspection of the golden note, you may notice that the first letter of each word cycles through the letters ISBN: ISBN = International Standard Book Number!

### The algebra bit

The 2nd note has a string of letters and numbers, but we do not know what the letters stand for. However we have some clues to solve them…

What is A?

The first equation (K + D)2 = A shows us that A must be a square number. The only possibilities between 1-9 are 1,4, or 9.

K and D must be also be between 1-9 and they must be different. The smallest possible choice here is that K and D are equal to 1 and 2 in some order, but A=1 or A=4 are too small to accept even the smallest valid values for K+D. Therefore A=9 which implies that K + D = 3 (incidentally also the smallest possible sum).

What are K and D?

Since we know that K+D=3, we have that either:

• K=1 and D=2 or;
• K=2 and D=1

If K=1, by the second equation C/F = 1, but this means that C=F which is a contradiction, since each letter must represent a different digit. Therefore, K=2 and D=1.

What is H?

Using the 3rd equation, with A=9 and K=2, we see that A-H=K implies that H=7.

What is C?

By the 4th equation: H+D=C, with H=7, D=1, we have that C=8

What is F?

By the 2nd equation: C/F = K, with C=8, K=2 we have that F=4.

Conclusion:

Now that we have found what each letter represents, we can see that the string of numbers is 9781444727296! This is the ISBN number for the book 11/22/63 (Stephen King) which is the date of the last bank heist! (Apologies for the Americanness of the date).