57th IMO in Hong Kong
+ 2 H K I 0 O O 5 M 1 I N N 7 O 6 N G G
The above represents a cryptogram , each letter represents a distinct digit, and each leading digit is non-zero. Find the number of possible solutions to this cryptogram.
Image Credit: Queen Elizabeth Stadium, Hong Kong. 5 July, 2016.
IMO scores have been released. Congratulations to the medalists and top-scoring teams, and thanks to each and every team for joining us in this meaningful event.
The answer is 48.
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2 solutions
Right , but maybe you should be a little more explicit in some steps.
But cute problem anyway.
Hey, where can the results of the IMO be seen? Do you know? Thanks!
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Mark coordination is in progress right now :)
I suppose on the official IMO page and on the official Hong Kong imo page too.
You can search it with google suppose you'll find it easily but the results aren't published yet anyway.
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Oh, if the results aren't out yet, then that explains it. :)
Oh my, I am soooo close!!
What are the 48 solutions? Can you list them all plz
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the solutions in the form KHIMGNO are: 5284170, 6384170, 9684170, 6384270, 9684270, 5284370, 9684370, 6384570, 9684570, 5284670, 5284970, 6384970, 5284061, 5284361, 5284761, 5284961, 6384052, 9684052, 6384152, 9684152, 9684352, 6384752, 9684752, 6384952, 6384025, 9684025, 6384125, 9684125, 9684325, 6384725, 9684725, 6384925, 5284016, 5284316, 5284716, 5284916, 5284107, 6384107, 9684107, 6384207, 9684207, 5284307, 9684307, 6384507, 9684507, 5284607, 5284907, and 6384907
The solutions: 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7 8 4 7 8 4 7 8 4 7 8 4 7 8 4 6 8 4 6 8 4 6 8 4 6 8 4 1 8 4 1 8 4 1 8 4 1 8 4 0 8 4 0 8 4 0 8 4 0 8 4 7 8 4 7 8 4 7 8 4 7 8 4 5 8 4 5 8 4 5 8 4 5 8 4 2 8 4 2 8 4 2 8 4 2 8 4 0 8 4 0 8 4 0 8 4 0 8 4 7 8 4 7 8 4 7 8 4 7 8 4 5 8 4 5 8 4 5 8 4 5 8 4 2 8 4 2 8 4 2 8 4 2 8 4 0 8 4 0 8 4 0 8 4 0 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 2 0 1 7 8 0 8 0 8 0 8 0 8 1 8 1 8 1 8 1 8 6 8 6 8 6 8 6 8 7 8 7 8 7 8 7 8 0 8 0 8 0 8 0 8 2 8 2 8 2 8 2 8 5 8 5 8 5 8 5 8 7 8 7 8 7 8 7 8 0 8 0 8 0 8 0 8 2 8 2 8 2 8 2 8 5 8 5 8 5 8 5 8 7 8 7 8 7 8 7 2 7 0 1 2 7 0 3 2 7 0 6 2 7 0 9 2 6 1 0 2 6 1 3 2 6 1 7 2 6 1 9 2 1 6 0 2 1 6 3 2 1 6 7 2 1 6 9 2 0 7 1 2 0 7 3 2 0 7 6 2 0 7 9 3 7 0 1 3 7 0 2 3 7 0 5 3 7 0 9 3 5 2 0 3 5 2 1 3 5 2 7 3 5 2 9 3 2 5 0 3 2 5 1 3 2 5 7 3 2 5 9 3 0 7 1 3 0 7 2 3 0 7 5 3 0 7 9 6 7 0 1 6 7 0 2 6 7 0 3 6 7 0 5 6 5 2 0 6 5 2 1 6 5 2 3 6 5 2 7 6 2 5 0 6 2 5 1 6 2 5 3 6 2 5 7 6 0 7 1 6 0 7 2 6 0 7 3 6 0 7 5 5 7 0 1 5 7 0 3 5 7 0 6 5 7 0 9 5 6 1 0 5 6 1 3 5 6 1 7 5 6 1 9 5 1 6 0 5 1 6 3 5 1 6 7 5 1 6 9 5 0 7 1 5 0 7 3 5 0 7 6 5 0 7 9 6 7 0 1 6 7 0 2 6 7 0 5 6 7 0 9 6 5 2 0 6 5 2 1 6 5 2 7 6 5 2 9 6 2 5 0 6 2 5 1 6 2 5 7 6 2 5 9 6 0 7 1 6 0 7 2 6 0 7 5 6 0 7 9 9 7 0 1 9 7 0 2 9 7 0 3 9 7 0 5 9 5 2 0 9 5 2 1 9 5 2 3 9 5 2 7 9 2 5 0 9 2 5 1 9 2 5 3 9 2 5 7 9 0 7 1 9 0 7 2 9 0 7 3 9 0 7 5
7 + O + 6 + N + G = G ⇒ O + N = 7 o r 1 7 5 + M + 1 + I + N + 2 o r 3 = N ⇒ 3 0 > 8 o r 9 + M + I > 2 0 I + 2 + O = O ⇒ I = 8 ⇒ O = 8 a n d N = 8 ⇒ O + N = 7 2 + H + 1 + K ⇒ H + 3 = K 5 + M + 1 + 8 + N + 2 = N ⇒ M = 4 G = a n y t h i n g e l s e
Given the above conditions, there are only 48 solutions that fit the equation.