Puzzle 437
Here is a curious grid! The sums of the shapes are shown at the end of each row, and at the bottom of each column.
What is the missing sum, and what is each shape worth?
Puzzle Copyright © Kevin Stone
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Hint
Look at the first and third columns first.
Answer
The missing sum is 40.
Circle = 12
Star = 3
Square = 7
Triangle = 9
Reasoning
Looking at Column 1 and Column 3 we have:
[1] Square + Star + Circle + Square = 29
[2] Square + Square + Triangle + Star = 26
If we subtract [1] − [2] we get:
[3] Circle − Triangle = 3
And Row 3 is:
[4] Circle + Circle + Triangle + Circle = 45
If we add [3] + [4] we get:
Circle + Circle + Circle + Circle = 48
So, Circle = 12.
Using [3] we find that Triangle = 9.
Using Column 2 we find that Star = 3.
Using Row 1 we find that Square = 7.
Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.
The columns add to: 29 + 36 + 26 + 40 = 131.
The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.
In total, there are:
5 Squares = 5 x 7 = 35
5 Circles = 5 x 12 = 60
3 Stars = 3 x 3 = 9
3 Triangles = 3 x 9 = 27
Which is also a total of 131.
So all of the totals are the same, as expected.
Puzzle 439
Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 4p, 5p, 7p, 12p, and 19p (just the five different values).
For three denominations of stamps, I was asked to buy six of each. For the other two denominations. I was asked to buy ten of each.
Unfortunately, I forgot which I was supposed to buy six of, and which to buy ten of!
Luckily I had been given the exact money required to buy the stamps, £3.50, so the shopkeeper was able to work out the stamps I needed.
Which stamps did I have to buy?
Puzzle Copyright © Kevin Stone
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Hint
I bought at least 6 of each stamp.
Answer
Six lots of 4p, 7p, and 19p, and ten lots of 5p, and 12p.
Reasoning
For three denominations of stamps, I was asked to buy 6 of each, and for the other two denominations, I had to buy 10 of each.
So I had to buy at least 6 of all five denominations.
This would be for a total of 6 x (4 + 5 + 7 + 12 + 19) = 282p = £2.82.
The remaining 68p has to buy the remaining 8 stamps, 4 of each of the two remaining denominations.
If we just bought 1 of each of the two remaining denominations they would have cost 68 ÷ 4 = 17p.
So the two remaining denominations must have been 5p and 12p.
Double-Checking
6 x 4 = 24
10 x 5 = 50
6 x 7 = 42
10 x 12 = 120
6 x 19 = 114
For a total of 24 + 50 + 42 + 120 + 114 = 350p = £3.50.
Puzzle 440
What letter comes next in this sequence:
M · V · E · M · J · ?
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Hint
Look to the skies for the answer.
Answer
S.
From Saturn.
Reasoning
These are the initial letters of the planets.
M = Mercury
V = Venus
E = Earth
M = Mars
J = Jupiter
S = Saturn
