Puzzle 5
Unluckily, last week I lost my measuring tape. It was unlucky as I had to measure Billy's toy box.
Luckily though I could remember that the top had an area of 720 square inches, the side was 800 square inches, and the end was 360 square inches.
What were the true dimensions of the toy box?
Puzzle Copyright © Kevin Stone
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Hint
A little algebra might help.
Answer
Width=40, height=20, depth=18.
Reasoning
If we call the height H, the width W and the depth D we have:
H x W = 800
H = 800 ÷ W (1)
W x D = 720
W = 720 ÷ D (2)
H x D = 360
H = 360 ÷ D (3)
Using (1) and (3) we have:
800 360
——— = ———
W D
800 x D = 360 x W
Using (2):
800 x D = 360 x 720
———
D
800 x D2 = 259,200
D2 = 324
D = 18
Using (2), W = 40.
Using (1), H = 20.
Puzzle 6
At the annual BrainBashers puzzle discussion conference, 20 people attended.
At the start of the conference, each person shook hands with every other person, how many handshakes took place in total?
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Hint
How many hands did the first person shake?
Answer
190.
The first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc: 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 190.
Puzzle 7
Billy has twice as many sisters as brothers.
His sister, Frankie, has one more sister than she has brothers.
How many boys and girls are there in the family?
Puzzle Copyright © Kevin Stone
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Hint
The answer isn't very large at all.
Answer
There are four boys and six girls in the family.
If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b - 1) = g.
And his sister, Frankie, has one more sister than she has brothers, so g - 1 = b + 1.
2(b - 1) = g [1]
g - 1 = b + 1 [2]
Using [1] in [2] gives:
2(b - 1) - 1 = b + 1
Expanding the bracket gives:
2b - 2 - 1 = b + 1
Simplifying the left hand side gives:
2b - 3 = b + 1
Add 3 to each side gives:
2b = b + 4
Subtract b from both sides gives:
b = 4
Using b = 4 in [1] gives:
2(4 - 1) = g
6 = g
Puzzle 8
Can you find every occurrence of the word MAY that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word MAY appears 39 times.
Answer
The word MAY appears 39 times.
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