Puzzle 6
Start in the bottom left corner and move either up or right, one square at a time, adding up the numbers. What is the largest total you can make?
5
2
5
4
1
7
6
1
7
3
5
9
4
1
5
2
3
8
3
2
3
1
4
9
6
Note: this puzzle is not interactive, and the numbers cannot be clicked.
Puzzle Copyright © Kevin Stone
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Answer
The largest total that can be made is 38.
Puzzle 7
A local school teacher wanted to share 703 sweets equally between the pupils.
If there were more than 20, but fewer than 50 pupils, how many sweets did each receive?
Puzzle Copyright © Kevin Stone
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Hint
What numbers divide into 703?
Answer
The 37 pupils each received 19 sweets.
Reasoning
703 can only be broken down into 19 x 37, it has no other factors.
Puzzle 8
Alex's child, Drew, is exactly one fifth of Alex's age. In 21 years, Alex will be exactly twice Drew's age. How old is Drew now?
Billie is exactly seven times the age of his child, Glen. In 8 years, Billie will be three times the age of Glen. How old is Glen now?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answers
Drew is 7 years old.
Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).
Drew is currently one fifth of Alex's age, so:
(1) A = D x 5
In 21 years, Alex will be twice their age, so:
(2) A + 21 = (D + 21) x 2
Using (1) in (2) gives:
A + 21 = (D + 21) x 2
5D + 21 = (D + 21) x 2
5D + 21 = 2D + 42
3D = 21
D = 7
So Drew is 7 (and Alex is 35).
Answer #2
The second question involves Glen (G) and Billie (B).
Billie is exactly seven times the age of Glen:
(3) B = G x 7
In 8 years, Billie will be three times the age of Glen, so:
(4) B + 8 = (G + 8) x 3
Using (3) in (4) gives:
B + 8 = (G + 8) x 3
7G + 8 = (G + 8) x 3
7G + 8 = 3G + 24
4G = 16
G = 4
So Glen is 4 (and Billie is 28).
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