DeepSeek V4 Pro vs Kimi K3 for bookkeeping

The difference is **£36.00** (£8,412.55 – £8,376.55).  

**Kind of error:** Transposition error (digits swapped).  

**Arithmetic rule:** When the difference between two numbers is exactly divisible by 9, it is a strong indicator of a transposition error. Here, £36 ÷ 9 = 4, pointing to a swap of digits that differ by 4 (in this case, 5 and 1 in £451 and £415).  

**Which side is wrong:** The cash book is wrong. The receipts for £451 and £415 have been entered in the opposite order to the bank credits.  

**How to prove it:** Check the original…

### 1. Difference

\[
£8,412.55-£8,376.55=\boxed{£36.00}
\]

The unpresented cheque and outstanding lodgement cancel:

\[
£8,412.55-£120+£120=£8,412.55
\]

So the unexplained difference remains **£36, with the bank balance higher than the cash book**.

### 2. Type of error indicated

£36 has the classic signature of a **digit-transposition error**:

\[
£451-£415=£36
\]

The rule is that a difference caused by transposing digits is divisible by 9:

\[
36\div 9=4
\]

For adjacent digits \(a\) and \(b\):

\[
(10a+b)-(10b+a)=9(a-b)
\]

More general…