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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: January 2012
Concatenation of Num3ers: (a(2n+1)+a(2n))^2 = a(2n+1) a(2n)
In mathematics, concatenation is the joining of two numbers by their numerals. That is, the concatenation of 123 and 456 is 123456. Concatenation of numbers a and b is denoted ab. Here are examples of quite remarkable numbers: 494 + … Continue reading
Why is 1+1=2 on the 20 greatest equation list?
Simplicity Respondents had many different criteria for greatness in equations. Half a dozen people were so impressed with simplicity that they proposed 1 + 1 = 2. “I know that other equations have done more, express greater power [and have … Continue reading
Magic Squares
In a magic square you have to add 3 numbers again and again the average sum of three numbers is 45/3 = 15 15 is called the magic number of the 3×3 square All the eight squares change into each … Continue reading
Permutations of Numbers
4356 = (1.5) * 6534 = (3/2) * 6534 85427136 = 2 * 42713568 = 4 * 21356784 = 6 * 14237856 using 3 permutations of the number itself (no digit 9 in all numbers) 142857 * 2 = 285714 … Continue reading
Pandigital numbers: numbers containing the digits 09
1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976 Table of n, a(n) for n = 1, .. ,1000 https://oeis.org/A050278/b050278.txt A = Pandigital numbers B = 2 * (a zeroless pandigital … Continue reading
Using all digits only once to make the num3er 9
(1) Ratios that use each of 9 digits 19 once 57429 ———— = 9 6381 58239 ———— = 9 6471 75249 ———— = 9 8361 (2) Ratios that use each of 10 digits 09 once 97524 ———— = 9 10836 … Continue reading
Using digits 1 to 9 only once to make the num3er 8
See also: Using all digits from 1 to 9 only once to make 2 (Part 4) Using all digits from 0 to 9 only once (Part 3) Using all digits 0 to 9 only once to make a sum equal … Continue reading
Using digits 1 to 9 only once to make 3, 4, 5, 6, 7
17469 ————– = 3 5823 17496 ————– = 3 5832 15768 ————– = 4 3942 17568 ————– = 4 4392 23184 ————– = 4 5796 31824 ————– = 4 7956 13485 ————— = 5 2697 13845 ————— = 5 2769 … Continue reading
Factorials
0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 … Continue reading
Egyptian fractions
The number of representations of one as a sum of unit fractions: 1 = 1/1 n = 2: 1 = 1/2 + 1/2 n = 3: 1 = 1/a + 1/b + 1/c 1 = 1/2 + 1/3 + 1/6 … Continue reading