Do You Know: There Are Happy Numbers And Sad Numbers In Mathematics!
Mathematics has always been a mystery for a majority of people, while it’s been fun to those who play with it. There are few things related to Mathematics that are really enjoyable. For example, take Happy Numbers and sad Numbers! You might be wondered to know that there are several numbers in Mathematics which are stated as Happy and Sad. Well, while numbers do not feel emotion, people do respond emotionally when numbers behave consistently in surprising and amusing ways. Let’s take a look at them!
What is a Happy Number?
In recreational mathematics, the so-called “happy numbers” and “unhappy numbers” are integers that produce particular sequences when you repeatedly square the number’s digits and compute the sum of those squares.
Confused? Let me explain in detail for you!
Consider any positive integer and sum the square of the individual digits. Continue the same process until it reaches the digit 1. If the number equals 1, then it is a happy number. If not, it is an unhappy or sad number.
To get a clear idea of the concept, let us consider an example.
It comes down to the number 1, so that means 32 is a Happy Number! (It also means that 13 and 10 are Happy Numbers as well, right?)
The 143 happy numbers up to 1,000 are:
1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, 490, 496, 536, 556, 563, 565, 566, 608, 617, 622, 623, 632, 635, 637, 638, 644, 649, 653, 655, 656, 665, 671, 673, 680, 683, 694, 700, 709, 716, 736, 739, 748, 761, 763, 784, 790, 793, 802, 806, 818, 820, 833, 836, 847, 860, 863, 874, 881, 888, 899, 901, 904, 907, 910, 912, 913, 921, 923, 931, 932, 937, 940, 946, 964, 970, 973, 989, 998, 1000
Well, how many times do you have to go through that cycle? What if it never comes down to 1? How will you know?
Answer: If it never comes down to 1, it will come down to 4 instead. (Presumably, that’s a UN-happy number!)
So here’s an example of an Unhappy Number:
