I think this puzzle must be wrong, because I can’t figure it out logically.
The trams in Melbourne, since changing ownership, are trying to be customer friendly, and to occupy our brains they’ve put some brain-teaser graphical puzzles on the walls. One of them is this one below, which actually uses little patterned circles for the mysterious numbers…
Anyways, the question mark is the answer required, but really just trying to figure out which digit goes where is hard enough.
If you look you will see that as rows 2 and 3 are only one different in answer, that means that the two characters that vary in the equation must also be only one different, which is what messes me up, because then I can’t get the first column to add up to 14
Any help would be grateful. (I suspect it’s either wrong, or a trick question)
Column 1 and column 3 have the same symbols in them – so that would be the same sum below (14… or -14, if you are counting the negative signs).
However, as rjk says, this problem is not valid. This is basically a system of equations, easier reading if you change the symbols to variables like x, y, etc. Same kind of thing. And this set of equations with these answers is not possible. Here it is rewritten with variables to make it easier:
x + y - z = 1
y + w - x = 5
z + w - x = 6
x + z - y = 4
Take the two that you cited, lines 2 and 3:
y + w - x = 5
z + w - x = 6
Subtract the second equation from the first, and you get:
y - z = -1 (also can say z - y = 1)
Plug this fact into the first equation:
x + y - z = 1 (and we know y - z is -1)
yields
x + -1 = 1
yields
x = 2
So rewrite the four equations, plugging 2 in for x:
2 + y - z = 1
y + a - 2 = 5
z + a - 2 = 6
2 + z - y = 4
simplifies to:
y - z = -1
y + a = 7
z + a = 8
z - y = 2
The first and last equations are now contradictory
y - z = -1 (already established)
z - y = 2 (nope... we already said z - y = 1)
I speculate that either the last 4.5 or the final 4 was copied down incorrectly. My money’s on the final 4.5 being wrong; they could have put some new and unknown symbol there and it would have been calculable as 3.5 and the whole thing would work (and the answer would be 13, rather than 14)
I checked the puzzle. I was right, it was copied down correctly. But the answer (it’s given, inverted, in tiny type) said ‘13’ so I think Sengkelat’s guess is probably right.
Now I’m going to email them and point out that putting up puzzles that are incorrectly made just drives people insane. You definitely don’t want insane tram passengers.
I think the problem with the puzzle solutions may be the differences in the symbols found above the numbers on the top row of your keyboard. (You do realize the symbols are based on your keyboard, right?)
I agree the problem must be wrong. Here’s another reason why. Turning those symbols into…well…other symbols, you get
a + b - c = 1
b + d - a = 5
c + d - a = 6
a + c - b = 4
14 15 ?
Take rows 1 and 4.
a + b - c = 1
a + c - b = 4
Add them together and you get 2a= 5 or a = 2.5
Take rows 1 and 3
a + b - c = 1
c + d - a = 6
Add them together and you get d+b = 7
OK, now look at row 2. If d+b = 7 and a = 2.5 then d + b - a must equal 4.5. It doesn’t. The problem says it equals 5. Ipso ergo: mathee no good.
