PASSION
=
KISS
If each letter represents a different digit from 0 to 9, what is the value of KISS?
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I have came up with a analytical way of solving this. But it will be easier with the help of a spreadsheet. Let's start from the end. We know that the last digit of the product S × S is N . Since S = N , therefore, S = 0 , 1 , 5 , 6 and S = 2 , 3 , 4 , 7 , 8 , 9 . Now move on to consider [ I S S ] 2 , the product should have its last three digit be I O N . Let's do the calculation for I = 0 . . . 9 , and check if the third last digit of the product is I as in P A S S I O N .
ISS ION
022 484 FALSE
122 14884 FALSE
322 103684 FALSE
422 178084 FALSE
522 272484 FALSE
622 386884 FALSE
722 521284 FALSE
822 675684 FALSE
922 850084 FALSE
033 1089 TRUE
133 17689 FALSE
233 54289 TRUE
433 187489 TRUE
533 284089 FALSE
633 400689 TRUE
733 537289 FALSE
833 693889 TRUE
933 870489 FALSE
044 1936 FALSE
144 20736 FALSE
244 59536 FALSE
344 118336 TRUE
544 295936 FALSE
644 414736 FALSE
744 553536 FALSE
844 712336 FALSE
944 891136 FALSE
077 5929 FALSE
177 31329 FALSE
277 76729 FALSE
377 142129 FALSE
477 227529 FALSE
577 332929 FALSE
677 458329 FALSE
877 769129 FALSE
977 954529 FALSE
088 7744 FALSE
188 35344 FALSE
288 82944 FALSE
388 150544 FALSE
488 238144 FALSE
588 345744 FALSE
688 473344 FALSE
788 620944 FALSE
988 976144 FALSE
099 9801 FALSE
199 39601 FALSE
299 89401 FALSE
399 159201 FALSE
499 249001 FALSE
599 358801 FALSE
699 488601 TRUE
799 638401 FALSE
899 808201 FALSE
It can be seen that there are six acceptable cases. The case of ( 3 4 4 , 1 1 8 3 3 6 ) is unacceptable because I = O = 3 is unacceptable.
ISS ION
033 1089 TRUE
233 54289 TRUE
433 187489 TRUE
633 400689 TRUE
833 693889 TRUE
344 118336 TRUE (FALSE)
699 488601 TRUE
Now check the final round of [ K I S S ] 2 . We note that K < 4 , else [ K I S S ] 2 has 8 digits.
KISS PASSION
1033 1067089 FALSE
2033 4133089 TRUE
3033 9199089 FALSE
1233 1520289 FALSE
2233 4986289 FALSE
3233 10452289 FALSE
1433 2053489 FALSE
2433 5919489 FALSE
3433 11785489 FALSE
1633 2666689 FALSE
2633 6932689 FALSE
3633 13198689 FALSE
1699 2886601 FALSE
2699 7284601 FALSE
3699 13682601 FALSE
We see that there is only one solution, that is K I S S = 2 0 3 3 .
I did exactly same.
int find a number() { List<int> lst = new List<int>(); List<int> lst1 = new List<int>(); List<int> lst2 = new List<int>(); string str = "", str 1, str 2 = null; int tmp = 0; for (int i = 1; i <= 9; i++) { lst.Add(Convert.ToInt32(i.ToString().PadLeft(2, Convert.ToChar(i.ToString())))); } for (int k = 0; k < lst.Count; k++) { for (int i = 10; i <= 99; i++) { str = i.ToString(); str 1 = lst[k].ToString(); if (str 1.IndexOf(str.Substring(0, 1)) < 0 && str 1.IndexOf(str.Substring(1, 1)) < 0) { str 2 = str + str 1; tmp = (int)Math.Pow(Convert.ToInt32(str + str 1), 2); if (tmp.ToString().Length == 7 && tmp.ToString().Substring(2, 1) == tmp.ToString().Substring(3, 1) && tmp.ToString().Substring(4, 1) == str 2.ToString().Substring(1, 1) && tmp.ToString().Substring(1, 1) != tmp.ToString().Substring(2, 1)) { lst1.Add(tmp); lst2.Add(Convert.ToInt32(str + str 1)); } } } } return lst2[0]; }
Isn't the baby's expression cool?
yes!! Very suprised.
This is a number theory problem, though, not computer science. So I insisted on doing this manually and surprisingly it wasn't much work, it is enough to check ( KISS 2 = PASSION ) using ( m o d 1 0 0 ) and ( m o d 1 0 0 0 ) and after founding a possibility of O, N, I, S, S , going through the three possibilities of K each time (we have 3 1 6 2 ≥ KISS ≥ 1 0 0 0 ). This didn't take much time in my case. I still think it may be better to put this problem in the computer science section instead.
check different valid combinations until sqrt(passion)=kiss
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My Bruteforce solution. :D
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I also used programming to solve it after trying to get it manually. But from preliminary calculations, it was found that K < 4 , else [ K I S S ] 2 will have 8 digits. My program is just to find the cases of matching S 's in P A S S I O N and K I S S . The Python program is as follows:
for k in range(1,4):
1422 2022084
2033 4133089
2877 8277129
3266 10666756
From the solutions (shown above after the program) from the program, the only solution for P A S S I O N is 4 1 3 3 0 8 9 when K I S S = 2 0 3 3 .