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Likewise in the following example:<br />

The Tough Stuff Made Easy: Advanced Multiplication 191<br />

538<br />

346<br />

<br />

540 346 186,840<br />

2 346 692<br />

<br />

186,148<br />

(540 2)<br />

(346 6 9 10)<br />

When-All-Else-Fails Method<br />

When all else fails, I use the following method, which is foolpro<strong>of</strong><br />

when you can find no other method to exploit the numbers.<br />

In the when-all-else-fails method, the 3-by-3 problem is<br />

broken down into three parts: a 3-by-1, a 2-by-1, and a 2-by-2.<br />

As you do each computation, you sum the totals as you go.<br />

These problems are difficult, especially if you cannot see the<br />

original number. In my presentation <strong>of</strong> 3-by-3s and 5-by-5s, I<br />

have the problems written down, but I do all the calculations<br />

<strong>mental</strong>ly.<br />

Here’s an example:<br />

851<br />

527<br />

<br />

500 851 425,500<br />

27 800 21,600<br />

<br />

447,100<br />

27 51 1,377<br />

<br />

448,477<br />

In practice, the calculation actually proceeds as shown below.<br />

Sometimes I use the phonetic code to store the thousands digits

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