Brain Teasers
Fish, Planes, and Flags
David's father is in charge of decorating the 2-layer cake for Great Grampa's birthday. Great Grampa's birthday is on the Fourth of July, he used to be a pilot, and he loves fishing. David and his father have decided to decorate the sides of the bottom layer of the cake (measuring 9 in. * 15 in.) with fish and the sides of the top layer (6 in. * 9 in.) with airplanes. They are going to wrap a flag around each corner of both layers. Each decoration is 1 inch wide, and each flag is folded so that one-half inch of flag shows at each side of the corner.
Show one corner of one layer with the Polish flag in place, with 1/2 of the flag visible on each side.
"We need 2 inches between all decorations," says David's father. "Otherwise it will look too crowded."
How many decorations of each kind do David and his father need?
Show one corner of one layer with the Polish flag in place, with 1/2 of the flag visible on each side.
"We need 2 inches between all decorations," says David's father. "Otherwise it will look too crowded."
How many decorations of each kind do David and his father need?
Hint
Start with a diagram of the longest side, and plan the arrangement for that side. Don't forget the flags!Answer
David and his father need 8 flags, 12 fish, and 6 airplanes.David and his father will place 12 fish decorations along the bottom layer of the cake.
Each of the longer sides of the bottom layer measures 15 in. Allowing 1/2 in. at each end for the flags and 2 in. between all the 1 in. decorations, they can place 4 fish along each 15 in. side like this:
(flag) (fish) (fish) (fish) (fish) (flag)
1/2 in. +2 in. +1 in. +2 in. +1 in. +2 in. + 1 in. +2 in. +1 in. +2 in. + 1/2 in. = 15 in.
Each of the shorter sides of the bottom layer measures 9 in. They can place 2 fish along this short side:
(flag) (fish) (fish) (flag)
1/2 in. +2 in. +1 in. +2 in. +1 in. +2 in. + 1/2 in. = 9 in.
Altogether, they can fit 12 fish (4 + 4 + 2 + 2 = 12) along the bottom layer.
The longer side of the top layer is the same length as the shorter side of the bottom layer. David and his father can fit 4 (2 + 2) airplanes on the longer sides of the top layer.
On each 6-in. side of the top layer they can fit just 1 airplane, like this:
(flag) (plane) (flag)
1/2 in. + 2 in. + 1 in. + 2 in. + 1/2 in. = 6 in.
Altogether, they can fit 6 airplanes (2 + 2 + 1 + 1 = 6) on the top layer.
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