♣♣♣♣♣♣♣♣♣♣♣♣ The Mysterious Number 22 ♣♣♣♣♣♣♣♣♣♣♣♣ Select any 3-digit number with all digits different from one another. Write all possible 2-digit numbers that can be formed from the 3-digits selected earlier. Then divide their sum by the sum of the digits in the original 3-digit number. You should always get the same answer, 22. There ought to be a big resulting “Wow!” For example, consider the three-digit number 365. Take the sum of all the possible two-digit numbers that can be formed from these three digits: 36+35+63+53+65+56 = 308. The sum of the digits of the original number is 3 + 6 + 5 = 14. Then 308/14 = 22. ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● Math behind this: To analyze this unusual result, we will begin with a general representation of the number: 100x + 10y + z. We now take the sum of all the two-digit numbers taken from the three digits: (10x+y)+ (10y+x) + (10x+z) + (10z+x) + (10y+z) + (10z+y) =10(2x+2y+2z) + (2x+2y+2z) =11(2x+2y+2z) =22(x+y+z) which, when divided by the sum of the digits, (x+ y + z), is 22. Such a type of illustration shows the value of algebra in explaining simple arithmetic phenomena.
Posted on: Wed, 24 Dec 2014 08:49:23 +0000
Trending Topics
Recently Viewed Topics
© 2015