Give your friend a calculator or have them use a mobile phone’s calculator application. For most mobile phones, turn the phone sideways to get scientific mode or use options to convert the calculator view to scientific. Your task is to determine your friend’s answer without looking at their phone or calculator.
· Ask your friend to divide 1 by their 7-digit phone number (or any other large number of their choosing).
· Confirm with your friend that the answer is a very small number but they don’t have to say what the number is.
· Ask your friend to add 1 to this result.
· Confirm with your friend that the answer is 1.00000xxxxx. Your friend doesn’t have to relieve the answer; your question is just to confirm that your friend is proceeding correctly with the instructions.
· Now, ask your friend to raise this number to the power of their phone number. With most scientific calculators this is done by pressing the key “xy” or “^ “.
· Now you are going to let your friend know the answer without looking at their phone or calculator. The first six digits of the answer should begin 2.71828.
Example 1
Friend’s secret number: 760-1000
1/7601000 = 0.0000001315616366
Add this answer to 1:
1 + 0.0000001315616366 = 1.0000001315616366
Raise this number to the power of the original number, 7601000
1.0000001315616366 ^ 7601000 = 2.71828… (other digits follow depending on the original number).
Example 2
Friend’s secret number: 100-0000 (or 1,000,000)
1/1000000 = .000001
Add this answer to 1;
1 + .000001 = 1.000001
Raise this number to the power of the original number: 1,000,000
1.000001 ^ 1000000 = 2.71828…
For advanced thinkers - How does it work?
Many mathematical calculations based on logarithms and exponents are based on the mathematical constant e. The constant e is equal to 2.718281828459… (digits continue).
One of the definitions of e is it is the limit of the expression:
(1 + 1/n)n as n becomes large. Another way to express this is the quantity (1+1/n) to the power of n.
Let’s explore some examples. Use your calculator or mobile phone to follow:
Let n=1
(1+1/1)1 = (1+1) = 2
Let n=10
(1+1/10)10 = (1+.1)10 = 2.25937
Let n=100
(1+1/10)100 = (1+.01)100 = 2.70481
Let n=1000
(1+1/1000)1000 = (1+.001)1000 = 2.71692
Let n=10,000
(1+1/10000)10000 = (1+.0001)10000 = 2.71815
Let n=100,000
(1+1/100000)100000 = (1+.00001)100000 = 2.71826
Let n=1,000,000
(1+1/1000000)1000000 = (1+.000001)1000000 = 2.71828
You can see how the final answer is converging on a single number and this number is the constant known as e. All seven-digit phone numbers greater than 999,999 will produce the same answer to the first six digits of 2.71818. Depending on the calculator or mobile phone, ten-digit phone numbers should also work but might cause an error because some of the intermediate steps in the process produce numbers so small it could be beyond the device’s capability. That is why the trick is best limited to the seven-digit phone number.
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