Brain Teasers
The Troll Bridge 4
A bridge was guarded by an evil troll. The troll was very intelligent, but he was also a coward. He was afraid of anyone smarter than him. So every time anyone tried to cross the bridge, the troll would set up a test. If the traveler passed the test, he would be allowed to cross. Otherwise, the troll would eat him.
A traveler came across the bridge. The troll said, "You may only cross my bridge if you know the password." He then wrote an equation on a rock:
NOSIER
+ASTRAL
________
725613
"Each letter in the equation represents a different digit, and no letter represents zero," said the troll. "The letters in the password represent 725613."
So, what is the password?
A traveler came across the bridge. The troll said, "You may only cross my bridge if you know the password." He then wrote an equation on a rock:
NOSIER
+ASTRAL
________
725613
"Each letter in the equation represents a different digit, and no letter represents zero," said the troll. "The letters in the password represent 725613."
So, what is the password?
Hint
1. There are nine different letters in the troll's equation, so nine digits in total are used. Since no letter represent zero, the nine digits used are obvious - just not the letter each one represents.2. This teaser requires some trial and error, but it can be minimized by looking at the two leftmost columns of the troll's equation.
Answer
The password is INLETS.If N+A=7, then either O+S=2, or 1+O+S=2, meaning that O+S=1. But the two lowest digits used are 1 and 2, so the lowest possible sum of two letters is 3. Therefore, 1+N+A=7, which means that N+A=6 and O+S equals 11 or 12. Either one of N and A is 1 and the other is 5, or one is 2 and the other is 4.
If R+L=3, then one of R and L is 1 and the other is 2. But since one of 1 and 2 must be either N or A, this cannot work, so R+L must equal 13. Therefore, 1+E+A equals 11, and E+A equals 10.
Since R+L=13, then R and L must be, in some order, 4 and 9, 5 and 8, or 6 and 7.
If N=1 and A=5, then E must equal 5. But since A and E need to have different values, this cannot work.
If N=5 and A=1, then E=9. R and L must be 6 and 7 in some order.
If N=2 and A=4, then E=6. R and L must be 5 and 8 in some order.
If N=4 and A=2, then E=8. R and L must be 6 and 7 in some order.
Since 1+I+R equals 6 or 16, I+R equals 5 or 15. Since R can only equal 5, 6, 7, or 8, I+R+15, so R cannot equal 5. Therefore:
If N=5, then R cannot be 6 because I would equal 9, and E=9. So R=7, L=6, and I=8.
If N=2, then since R cannot be 5, R=8, L=5, and I=7.
If N=4, then R cannot be 7 because I would equal 8, and E=8. So R=6, L=7, and I=9.
Since 1+S+T equals 5 or 15, S+T equals 4 or 14. If S+T=14, then S and T must be 5 and 9, or 6 and 8, in some order. But each of our three scenarios has a letter for at least one of 5 and 9, as well as one for 8. So S+T=4, S and T are 1 and 3 in some order, and O+S=12.
If S=1, then O=11. But since each letter represents only one digit, S=3, T=1, and O=9.
If N=5, then A=1. But since T=1, this cannot work.
If N=4, then I=9. But since O=9, this cannot work.
We are left with one possible scenario:
T=1, N=2, S=3, A=4, L=5, E=6, I=7, R=8, and O=9.
Therefore, 725613=INLETS.
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