During a recent gymnastics gala, four athletes competed in three events, the vault, the beam, and the floor.
Chris came third on the floor. The athlete who came second in the vault won the beam event. The athlete who came second on the beam won the floor. Emery beat Alex in every event. The athlete who won the vault came second on the floor. Billie came last in the vault.
Can you determine who finished where in each event?
Hint
Could Alex have come first or second in any event?
Answer Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex
Reasoning
By (1), Chris came third on the floor. By (6), Billie came last in the vault.
Vault Beam Floor
#1
#2
#3 Chris
#4 Billie
By (2), the athlete who came second in the vault won the beam event, let's mark these as X.
By (3), the athlete who came second on the beam won the floor, let's mark these as Y.
By (5), the athlete who won the vault came second on the floor, let's mark these as Z. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Chris
#4 Billie
By (4), Emery beat Alex in every event, therefore Alex can't have won any event, nor come second (because of X, Y, and Z). So, Alex came third on the vault, and last on the floor. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Alex Chris
#4 Billie Alex
Looking at the vault, Z can't be Chris because Z came second on the floor (but we know Chris came last). So, Z must be Emery, and X is Chris. Vault Beam Floor
#1 Emery Chris Y
#2 Chris Y Emery
#3 Alex Chris
#4 Billie Alex
Looking at the floor, Y is Billie. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Chris
#4 Billie Alex
By (4), Emery beat Alex on the beam. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex
??
Puzzle 59
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?
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 60
Take a set of three letters from the left column, and a set of three letters from the right column and merge them together, without changing the order of the letters in each half (matching sets might not be on the same row).
Example 1: wmb + oat and mat + wob both equal wombat.
Example 2: rbt + abi and ait + rbb both equal rabbit.
Can you find the six animals that have been split in half?
cyo aru
wls dne
ear fee
oky ote
rrt jar
agu bve
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