Seven Eight Nine
+ E S I N E G I T V H N E E T E N N
Solve the cryptarithm above, and find E + I + G + H + T + N + S + V .
The answer is 35.
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4 solutions
close to mine, from those equations you can also know that 1<E<9 and E=I+N-9, helping to asume that E is a low value,
Sir, I'm admiring you how you got it, for me, I think even I solve it the whole day I cannot arrive at the answer. I have only some inquiry on your solution, at first, how did you know that (T,E) = (1,9), isn't the 10 has many additives, like (3,7), (2,8), (6,4) and so on, or It can also be (0,0), for the N to retain, then how did you know that these are 1 and 9, and the same also for other letters/variables. thank you sir and I'm hoping for your response.(:
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its more a try and see than an straight method what you need to solve this problem; i remember a couple of those deductions: eache letter is a number from 0 to 9 no letter has the same value than another since E+T=10 and E cannot be equal to T E and T cant be 0 or 5 making T be a function of E: T=10-E S=E+1, since S<10, E+1<10; E<9 and you know that I+N+ (highly possible) 1 = E + 10, (otherwhise the last addition would give another E instead of an S) since E cant be 0, I+N NEED to be bigger than 9
if you check the convinations of different numbers that are true and no number is repeated, youll see that it get higher probabilities for lower values
for example: if (I,N) where (8,9) or (9,8), the value for E would be 8, repeating the number, making false that E=8, now you got one less value to check and if you follow this way to check, end up "seeing" that there are more chances for E to be a low value, the rest is solved like a sudoku
since T not equal to E it cant take value (0,0)
I think you should read that line carefully I have written all the possible additives of (T,E) . :)
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thank you sir, what I can't understand is how you arrived at that number(1,9). thank you to Mr. Frankenstein, he elaborated it to me, though, still, it's hard for me to solve the problem like that if I encountered another one. (;
Mr Mohtasim Nakib what are the numbers 27058,4742,824,32624 Represent and how did you figure it out ,could you please explain it to me ?
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27058 is the top number (EIGHT), 4742 is the second one (NINE), 824 is the third one (TEN) and 32624 is the sum (SEVEN)
T+E+N=N then how is T+E=10??? I didn't get that. Can you please explain? If cancellation can be applied then it must be T+E=0. Correct me if I'm wrong
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Think of T+E+N as x+y+z. Since x+y+z=z we subtract z from both sides. This leaves us with x+y=0. In this scenario the only way to achieve 0 in the ones column is to get some multiple of 10. Given only two integers the only possible outcome that can be a multiple of ten is ten, therefore we know that T+E must equal 10.
How can u be sure that T+E=10, it can be a multiple of 10. Please elaborate why u assume that. I know this type of problem can be solve by taking such assumption, but is there any other generic way to solve this problem.
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first thing: each letter has a decimal value and none can be repeted; therefore
T,E,N <10
as a fact, the addition T+E+N < 30, and since no value can be repeated, picking the bigger ones give's you the maximum limit: 9+8+7=24; so
T+E+N < 24
since T+E+N=N and a value to carry(0.1 or 2): you make 3 assumptions:
1) T+E=0. Since T=/=E, so T+E>0
2) if the carry is equal 2, T+E=20, but since T,E <10, the maximum value of T+E=17
3) because the other options are out of the limits / conditions, the only viable option is E+T=10
But a letter can represent a single digit only. So, it should be 10.
It took me 4 5 minutes solve the cryptarithm E = 2 , I = 7 , G = 0 , H = 5 , T = 8 , N = 4 , S = 3 , V = 6
E + I + G + H + T + N + S + V = 3 5
Please post ur method!!
How you got that ? explain me please :D
Hey Paola, could u tell me about ur approach to solve that problem. Very thankful to u in advanced.
tbh, I just guessed.
Hey Paola can u please tell me, from where did u come to know the values of alfabets??...
pls say how ?
Why this isn't the solution of the cryptarithm...
-
Where..
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- E=8. I=1. G=4. H=2. T=2.
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- N=7. S=8. V=8.
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- ?????????
The equation is 10000 S + 100 V = 9001 E + 1100 I + 1010 N + 101 T + 100 G + 10 H;
27058
4742
824
32624
2 + 7 + 0 + 5 + 8 + 4 + 3 + 6 = 35
Mr Lu i understand how did this equation mean but what are the numbers 27058,4742,824,32624 Represent and how did you figure it out ,could you please explain it ?
I decided to try to solve this problem by finding what where the 3 digits that weren't in the cryptarithm and deduced that neither 0, 9 or 1 could be used in the problem. Went rapidly as those where the obvious firsts digits to try.
I can not follow your line of reasoning, especially since 0 is in the cryptarithm...
my way of solution is a little boring.
T + E + N = N so T + E = 10 . there are (T,E)=(1,9),(9,1),(2,8),(8,2),(3,7),(7,3),(4,6),(6,4) possible pairs.
H+N+E+1 = E so H+N+1 =10 , H+N =9 . there are (H,N)=(1,8),(8,1),(2,7),(7,2),(3,6),(6,3),(4,5),(5,4) possible pairs.
and E+1=S.
starting by taking possible pair of(H,N) and attempting each pair I find
27058+4742+ 824=32624
so the ans is:
2+7+0+5+8+4+3+6 = 35