The Power of Forgetting (20 page)
Read The Power of Forgetting Online
Authors: Mike Byster
For more of these types of games, go to
http://intelligencetest.net/part1
.
Seeing patterns in geometric shapes and strings of letters is one thing, but what about seeing patterns in traditional math equations? I’ve already given you a few math shortcuts in this book, but the ones here were designed specifically to help you think outside the box. How? They break all the rules that
you’ve probably been taught when it comes to these types of equations.
I’ll give you nine shortcuts in this section. By following the directions and doing a little mental math, you should be able to solve some seemingly complex problems rather easily. The challenge will come when you know all of the shortcuts and then are asked to solve problems using one of the patterns and must first figure out which one to use, then apply it quickly. (You can use notes or work from memory.)
Example:
57 × 57
Step 1:
Always start with the number 25. Now add the ones digit (7) to it (25 + 7 = 32).
Step 2:
Square the ones digit (7 × 7 = 49). Tack that number onto the answer from step 1.
Answer:
57 × 57 = 3,249
If the number from step 2 is less than 10, you have to put a 0 in front of it.
Example:
53 × 53
Step 1:
25 + 3 = 28
Step 2:
3 × 3 = 09 (Since 9 is less than 10, put a 0 in front of it.)
Answer:
53 × 53 = 2,809
Example:
65 × 65
Step 1:
Take the tens digit (6) and multiply it by the number one greater than it (7) (6 × 7 = 42).
Step 2:
Tack 25 onto the end of the number from step 1.
Answer:
65 × 65 = 4,225
Example:
75 × 85
Step 1:
Take the smaller tens digit (7) and multiply it by the number that is one greater than the larger tens digit (8) (8 + 1 = 9; 7 × 9 = 63).
Step 2:
Tack 75 onto the end of the number from step 1.
Answer:
75 × 85 = 6,375
Example:
65 × 85
Step 1:
Take the smaller tens digit (6) and multiply it by the number one greater than the larger tens digit (8) (8 + 1 = 9; 6 × 9 = 54).
Step 2:
Add 1 to the number from step 1 (54 + 1 = 55).
Step 3:
Tack 25 onto the end of the number from step 2.
Answer:
65 × 85 = 5,525
When you multiply two numbers in the nineties, in parentheses next to each number put how far away that number is from 100. Since 93 is 7 away from 100, and 96 is 4 away from 100, the problem 93 × 96 would be written like this: 93(7) × 96(4).
Example:
93(7) × 96(4)
Step 1:
Add up the numbers in parentheses (7 + 4 = 11) and subtract that number from 100 (100 − 11 = 89).
Step 2:
Multiply the two numbers in parentheses and tack that product onto the end of the number from step 1 (7 × 4 = 28).
Answer:
93 × 96 = 8,928
If the number from step 2 is less than 10, put a 0 in front of it.
Example:
97(3) × 98(2)
Step 1:
3 + 2 = 5; 100 − 5 = 95
Step 2:
3 × 2 = 06
Answer:
97 × 98 = 9,506
Example:
43 × 43
Step 1:
Start out with 15 and add the ones digit to it (15 + 3 = 18).
Step 2:
Figure out by how much the number you
are squaring (43) is less than 50 (50 − 43 = 7) and square that number (7 × 7 = 49). Tack that number onto the end of the number from step 1.
Answer:
43 × 43 = 1,849
If the number from step 2 is less than 10, put a 0 in front of it.
Example:
48 × 48
Step 1:
15 + 8 = 23
Step 2:
50 − 48 = 2; 2 × 2 = 04
Answer:
48 × 48 = 2,304
Example:
106 × 108
Step 1:
The first digit of the answer is always 1.
Step 2:
To get the next two digits, add the ones digits (6 + 8 = 14).
Step 3:
To get the final two digits, multiply the ones digits (6 × 8 = 48).
Answer:
106 × 108 = 11,448
If the number in either step 2 or step 3 is less than 10, put a 0 in front of it.
Example:
102 × 104
Step 1:
The first digit of the answer is always 1.
Step 2:
Add the ones digits together (2 + 4 = 06).
Step 3:
Multiply the ones digits (2 × 4 = 08).
Answer:
102 × 104 = 10,608
Example:
204 × 209
Step 1:
The first digit of the answer is always 4.
Step 2:
To get the next two digits, add the ones digits and double the product (4 + 9 = 13; 13 × 2 = 26).
Step 3:
To get the final two digits, multiply the ones digits (4 × 9 = 36).
Answer:
204 × 209 = 42,636
If a number from either step 2 or step 3 is less than 10, put a 0 in front of it.
Example:
207 × 201
Step 1:
The first digit of the answer is always 4.
Step 2:
7 + 1 = 8; 8 × 2 = 16
Step 3:
7 × 1 = 07
Answer:
207 × 201 = 41,607
Example:
71 × 51
Step 1:
Multiply the tens digits (7 × 5 = 35) and tack a 0 onto the end of that product (350).
Step 2:
Add the tens digits (7 + 5 = 12) and add that number to the number from step 1 (350 + 12 = 362).
Step 3:
Tack a 1 onto the end of the number from step 2.
Answer:
71 × 51 = 3,621
Example:
31 × 41
Step 1:
3 × 4 = 12. Tack on a 0 and you get 120.
Step 2:
3 + 4 = 7; 120 + 7 = 127
Step 3:
Tack a 1 onto the end.
Answer:
31 × 41 = 1,271
Can you perform a few more on your own? And without looking back at the steps I’ve given you for each type of pattern? I encourage you to go back one more time to each of the above steps. Aim to commit each pattern’s shortcut to memory, as this will force you to think outside the box and forget about traditional rules. Then, once you feel like you’re ready to tackle a few more on your own and no longer need to revisit the steps, turn to this section and see how fast you can solve the following problems.
| 54 × 54 = | 59 × 59 = |
| 85 × 85 = | 35 × 35 = |
| 55 × 65 = | 25 × 35 = |
| 25 × 45 = | 55 × 75 = |
| 95 × 94 = | 96 × 92 = |
| 46 × 46 = | 42 × 42 = |
| 103 × 105 = | 104 × 109 = |
| 206 × 205 = | 208 × 202 = |
| 41 × 61 = | 91 × 31 = |
You’ll find the answers to these equations at the end of the chapter.
I can’t reiterate enough the value of being able to think differently from the mainstream. While productive thinkers may be varied, they all have one feature in common: creativity. You might not think that playing a rebus game or learning a shortcut in math is going to help you in real-life situations where you want to access your creativity, but in fact practicing these types of brainteasers opens up areas of the brain that support inventiveness. We owe some of our most beloved inventions today to people who thought outside the box and took “accidents” in their daily work to the next level by asking themselves “outside” questions.
Take, for example, the microwave oven, which is now a standard appliance in most American households. When you Google the history of the microwave oven, you find a great story about how this now-ubiquitous machine came to be. In 1945 Percy Spencer was experimenting with a new vacuum tube called a magnetron while doing research for Raytheon Company. When his candy bar melted in his pocket, he took note of it and stopped to ask himself how this phenomenon could be applied elsewhere. Thinking outside the box, he tried another experiment with popcorn, and when the kernels began to pop, Spencer immediately saw the potential in this revolutionary process. In 1947 Raytheon built the first microwave oven, the Radarange, which weighed 750 pounds, was five and a half feet tall, and cost about $5,000. When the Radarange first became available for home use in the early 1950s, its bulky size and expensive price tag made it unpopular with consumers. But in 1967 a much more popular hundred-volt, countertop version was introduced at a price of $495. Today you can buy a microwave oven for under $100.
I’ll admit that I’m a big consumer of diet soda—much to my doctor’s chagrin. I don’t drink alcohol, and I don’t gamble, but I do drink a lot of diet soda pop. And I have a famous accident to thank. Saccharin, the oldest artificial sweetener, was accidentally discovered in 1879 by researcher Constantin Fahlberg, who was working at Johns Hopkins University in the laboratory of professor Ira Remsen. Fahlberg’s discovery came after he forgot to wash his hands before lunch. He had spilled a chemical on his hands, and it caused the bread he ate to taste unusually sweet. Had he not been thinking outside the box when he took that fateful bite, he might have missed the discovery entirely. In 1880 the two scientists jointly published the finding, but in 1884 Fahlberg obtained a patent and began mass-producing saccharin without Remsen. The use of saccharin became widespread when sugar was rationed during World War I, and its popularity increased during the 1960s and 1970s with the manufacture of Sweet’N Low and diet soft drinks. Today I’m among the millions who keep Fahlberg’s patent valuable. (To clarify: Several other artificial sweeteners have been developed since saccharin was discovered. Saccharin got a bad rap in the 1970s owing to exaggerated claims that it causes cancer, and it’s now outpaced by aspartame and sucralose in the market. Tab may be the only soda left that’s based on saccharin.)
I’ll give you one more example, well detailed by the folks at
www.HowStuffWorks.com
. In 1943 naval engineer Richard James was trying to develop a spring that would support and stabilize sensitive equipment on ships. When one of the springs accidentally fell off a shelf, it continued moving—and a lightbulb turned on over James’s head. He climbed out of his “box” and got an idea for a toy. His wife, Betty, came up with the name. When the Slinky made its debut in late
1945, James sold four hundred of the bouncy toys in ninety minutes. Today more than 250 million Slinkys have been sold worldwide.
The point I want to make is that no matter where you are or what you’re doing—whether you’re a cook, a CEO, a midlevel manager hoping to advance and land the corner office, or a stay-at-home parent with a part-time job as a blogger—things tend to happen that can result in surprising opportunities. People don’t necessarily stumble upon good fortune or luck. They come to situations and circumstances with a mind-set that prepares them to “get lucky.” As that old saying goes, success happens at the intersection of preparation and opportunity. And being able to think outside the box—to stop and ask yourself
why
or
how
as often as you can—is key to that preparation.
I should also point out that while few of us are going to invent the next big thing on par with the microwave or sliced bread, all of us will be faced with problems to solve that demand we think outside the box. This is true no matter what kind of job we have, where we live, or what resources we possess. When we take this skill to work or employ it at home in even the most mundane of habits and daily tasks, we can make life a whole lot easier. Don’t for a minute believe that thinking outside the box is reserved for the super artsy types who work in highly creative or technical jobs. I wish that this skill weren’t always so linked to innovation and creativity. I see it more as a necessary tool equal in importance to being able to read, write, and even
think
at all!
Only those who can routinely think outside the box go on to achieve what they set out to do in life. And sometimes those people’s goals have nothing to do with invention per
se. So the next time you’re wondering how thinking outside the box will help you, remember: This skill provides the foundation for all kinds of problem solving in virtually any type of setting. It also facilitates new opportunities that present themselves (often when you least expect it) and help you to take advantage of those possibilities. While I may have outlined historical examples of thinking outside the box in action, plenty of newer examples abound. Popular social-media technology, for instance, owes its origins to productive thinkers who took note of an opportunity and capitalized on it. Just look around you to see the fruits of someone else’s productive thinking outside the box at work. Every time you visit a Web site; buy a product; respond to an advertisement; read an engaging article, blog, or book; or compliment a co-worker for a job well done, chances are you’re recognizing the upshot of thinking outside the box. Pure and simple.
When the creative part of the brain begins to churn, it can be hard to stop it! And the rewards are limitless.
