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A man enters an expensive restraunt and orders a meal. When the waiter brings him his meal the man takes out a slip of paper and writes down 102004180, then leaves. The cashier hands the slip of paper to the cashier who understood it immediately. What did the slip of paper say?
Answer: I =1, 0=Ought, 2=To, 0=Owe, 0=Nothing, 4=For, 1=I, 8=Ate, 0=Nothing. I Ought To Owe Nothing For I Ate Nothing. 102004180
Solution:
When the celebrated German mathematician Karl Friedrich Gauss (1777-1855) was nine he was asked to add all the integers from 1 through 100. He quickly added 1 to 100, 2 to 99, and so on for 50 pairs of numbers each adding to 101. Answer: 50 X 101=5,050. What is the sum of all the digits in integers from 1 through 1,000,000,000? (That’s all the digits in all the numbers, not all the numbers themselves.)
Answer: The numbers can be grouped by pairs: 999,999,999 and 0; 999,999,998 and 1' 999,999,997 and 2; and so on.... There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then: (500,000,000 X 81) + 1= 40,500,000,001.
Solution:
Show Answer
The numbers can be grouped by pairs:
999,999,999 and 0;
999,999,998 and 1′
999,999,997 and 2;
and so on….
There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then:
(500,000,000 X 81) + 1= 40,500,000,001.
Show Answer
The numbers can be grouped by pairs:
999,999,999 and 0;
999,999,998 and 1′
999,999,997 and 2;
and so on….
There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then:
(500,000,000 X 81) + 1= 40,500,000,001.
999,999,999 and 0;
999,999,998 and 1′
999,999,997 and 2;
and so on….
There are half a billion pairs, and the sum of the digits in each pair is 81. The digits in the unpaired number, 1,000,000,000, add to 1. Then:
(500,000,000 X 81) + 1= 40,500,000,001.
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