Puzzle 18
If I give you seven apples, you will then have five times as many as I would then have.
However, if you give me seven apples, we will then both have the same number of apples.
How many apples do I currently have?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
I have 14 apples and you have 28 apples.
Reasoning
We can work this out with a little algebra. I have A apples and you have B apples, then
[1] 5 x (A − 7) = B + 7
[2] A + 7 = B − 7
From [1] we have:
5A − 35 = B + 7
[3] 5A = B + 42
From [2] we have:
[4] A + 14 = B
We can then use [4] in [3] to give:
5A = (A + 14) + 42
5A = A + 56
4A = 56
A = 14
Which gives B = 28 (by [4]).
Puzzle 19
Using the letters EEEEGGLLOOSS complete this grid. The grid reads the same across as down.
Note: this puzzle is not interactive, and the squares cannot be clicked.
Puzzle Copyright © Kevin Stone
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Hint
One of the words begins with the letter S.
Answers
| D |
O |
G |
S |
| O |
G |
L |
E |
| G |
L |
E |
E |
| S |
E |
E |
K |
Puzzle 20
What value of X makes the following correct:
Puzzle Copyright © Kevin Stone
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Hint
The answer is a whole number less than 10.
Answer
3.
Reasoning
We can multiply throughout by 12,
X X X X
- - - + - = -
X 2 4 12
to give:
12 − 6X + 3X = X
12 − 3X = X
12 = 4X
3 = X
As required.
Double-Checking
3 3 3 3
- - - + - = -
3 2 4 12
1 − 1.5 + 0.75 = 0.25
0.25 = 0.25, which confirms that 3 is correct.
