Brain Teasers
Magic Hourglass
Arrange the numbers 1 through 11 in the shape of an hourglass, as described below.
Three numbers in the first row (A, B, C), top of the hourglass
Two numbers in the second row (D, E)
One number in the third row (F), neck of the hourglass
Two numbers in the fourth row (G, H)
Three numbers in the fifth row (I, J, K), bottom of the hourglass
Arrange the numbers to meet the following criteria:
F is equal to the difference between D and E, and the difference between G and H
D is equal to the difference between A and B
E is equal to the difference between B and C
G is equal to the difference between I and J
H is equal to the difference between J and K
Three numbers in the first row (A, B, C), top of the hourglass
Two numbers in the second row (D, E)
One number in the third row (F), neck of the hourglass
Two numbers in the fourth row (G, H)
Three numbers in the fifth row (I, J, K), bottom of the hourglass
Arrange the numbers to meet the following criteria:
F is equal to the difference between D and E, and the difference between G and H
D is equal to the difference between A and B
E is equal to the difference between B and C
G is equal to the difference between I and J
H is equal to the difference between J and K
Answer
Ignoring mirror images, there are only two solutions.First row: A = 9, B = 4, C = 6
Second row: D = 5, E = 2
Third row: F = 3
Fourth row: G = 7, H = 10
Fifth row: I = 8, J = 1, K = 11
First row: A = 9, B = 5, C = 11
Second row: D = 4, E = 6
Third row: F = 2
Fourth row: G = 1, H = 3
Fifth row: I = 8, J = 7, K = 10
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