Gemini 3.1 Pro Preview vs Kimi K3 for bookkeeping

**1. Work out the difference**
The bank statement closing balance is £8,412.55. 
The cash book closing balance is £8,376.55. 
The difference is **£36.00** (£8,412.55 - £8,376.55). 
*(Note: The outstanding unpresented cheque and uncredited lodgement of £120.00 perfectly cancel each other out, so they do not affect this £36.00 difference).*

**2. What kind of error is it?**
This is a **transposition error** (specifically, reversing two adjacent digits when recording a number). 

**3. The arithmetic rule that identifies this class of error at a gl…

### 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…