Brain Teasers
Group Values
In each group each of the letters A through H has one of the eight values listed. No two letters have the same value. The simple arithmetic problems are clues for determining the values of each letter. The three groups are independent.
Group 1
2,5,6,8,10,13,15,21
H+D=G
E-C=D
H+G=A
F+H=C
E-F=G
B+E=A
Group 2
3,4,5,9,12,13,17,22
C-A=B
H+D=A
D+F=G
F-A=E
C-D=G
Group 3
4,5,6,10,11,14,15,20
B-G=H
A+E=C
F-C=H
D-B=A
A+H=G
E+F=D
Group 1
2,5,6,8,10,13,15,21
H+D=G
E-C=D
H+G=A
F+H=C
E-F=G
B+E=A
Group 2
3,4,5,9,12,13,17,22
C-A=B
H+D=A
D+F=G
F-A=E
C-D=G
Group 3
4,5,6,10,11,14,15,20
B-G=H
A+E=C
F-C=H
D-B=A
A+H=G
E+F=D
Answer
1. A=21, B=6, C=10, D=5, E=15, F=2, G=13, H=82. A=9, B=13, C=22, D=5, E=3, F=12, G=17, H=4
3. A=6, B=14, C=11, D=20, E=5, F=15, G=10, H=4
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Comments
Fun stuff! Good to have teasers like this here!
Great teaser! I used a "this is greater than that" method in conjunction with x=y, y=z, therefor x=z algebra. Fantastic teaser to get the ol' brain juices flowing.
Kudos. This took a bit of effort. At first glance, I thought it a simple substitution problem, but it -- or at least my approach -- turned out to be less formulaic. No simple explanation of method here. I suppose there are many -- most, I'm guessing, more simple than mine. I chose to first find the letter with the greatest value and then two equations within each list that totaled that value. From there, each group required slightly different observations to solve. Must have taken some effort to create. . I enjoyed it.
For anyone attempting to work the teaser, I should clarify that I first found the letter (within each group) that had the greatest value. To do this, first change any subtraction equations to addition equations (basic algebra). Then, just use the method "this is greater than that, so also greater than...." EG.) B = H + G; therefore B > H and G. D = A + B; therfore D > A, B, H, G. Now, within that same group, find two equations that each total the greatest value. These two equations and the sum (same for both) account for five numbers. You now only have three numbers left to assign letters. Use the same method for each group. It is at this point that each group requires slightly different observations to solve.
Great teasers. The first one took me quite some time. Set it up with a logic grid and used excel to help with all the calculations. The second two went quite a bit quicker.
Very nicely done!!
Very nicely done!!
To be totally honest this was one of the easiest teases I've seen in a while. It must be the way I think.
It was fun to crack ! Good one !
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