# Cryptic Combinations

## Solution

Page 1: Jackson Page 2: Isabella Page 3: Sebastian
Left 42
Right 37
Left 20
Left 25
Right 49
Left 9
Right 16
Left 43
Right 23
Left 33

## Explanation

First, follow the order of operations to find the numbers in each combination.

### The clues for the combination on page 1:

Turn left: (2² − 10) (2.6 + -9.6)

 Evaluate powers within parentheses. Complete operations within parentheses. (2² − 10) (2.6 + -9.6) (4 − 10) (2.6 + -9.6) (-6) (-7) Multiply and divide in order from left to right. (-6) (-7) 42

Turn right: (-46.3 − 28.7) + x

 Complete operations within parentheses. (-46.3 − 28.7) + x (-75) + x Multiply and divide in order from left to right. 25 + x 25 + 3 x 4 25 + 12 Add and subtract in order from left to right. 25 + 1237

Turn left: (9² − 1) x ()²

 Evaluate powers within parentheses. Complete operations within parentheses. (9² − 1) x ()² (81 − 1) x ()² (80) x ()² Evaluate powers. (80) x ()² (80) x Multiply and divide in order from left to right. (80) x 20

The combination for page 1 is:

Left 42
Right 37
Left 20

42 + 37 + 20 = 99

### The clues for the combination on page 2:

Turn left: (27.8 + 8.2) + (-6 x -8)

 Complete operations within parentheses. (27.8 + 8.2) + (-6 x -8) (36) + (48) Multiply and divide in order from left to right. (36) + (48) 9 + (48) Multiply and divide in order from left to right. 9 + (48) 9 + 16 Add and subtract in order from left to right. 9 + 1625

Turn right: (-8 + 2 − -10 + 3) (2² + 3 x 12)

 Evaluate powers within parentheses. First, complete operations within parentheses. Next, multiply and divide. Last, add and subtract from left to right. (-8 + 2 − -10 + 3) (2² + 3 x 12) (-8 + 2 − -10 + 3) (4 + 3 x 12) (-8 + 2 − -10 + 3) (4 + 3 x 12) (-8 + 2 − -10 + 3) (4 + 3 x 12) (-8 + 2 − -10 + 3) (4 + 3) (-6 + 10 + 3) (4 + 3) (+4 + 3) (4 + 3) (7) (7) Multiply and divide in order from left to right. (7) (7)49

Turn left: -8 (-9 +7)² ÷ (-19.8 + 17.8) − 7

 Complete operations within parentheses. -8 (-9 + 7)² ÷ (-19.8 + 17.8) − 7 -8 (-2)² ÷ (-2) − 7 Evaluate powers. -8 (-2)² ÷ (-2) − 7 -8 (4) ÷ (-2) − 7 Multiply and divide in order from left to right. -32 ÷ -2 − 7 16 − 7 Add and subtract in order from left to right. 16 − 79

Turn right: (15 ÷ ) − (3.4² − 2.56)

 Evaluate powers within parentheses. (15 ÷ ) − (3.4² − 2.56) (15 ÷ ) − (11.56 − 2.56) Complete operations within parentheses. (15 ÷ ) − (11.56 − 2.56) (15 x ) − (11.56 − 2.56) () − (11.56 − 2.56) (25) − (9) Add and subtract in order from left to right. (25) − (9)16

The combination for page 2 is:

Left 25
Right 49
Left 9
Right 16

25 + 49 + 9 + 16 = 99

### The clues for the combination on page 3:

Turn left: (-12 + 4)² − 3 (6 + 1)

 Complete operations within parentheses. (-12 + 4) ² − 3 (6 + 1) (-8)² − 3 (7) Evaluate powers. (-8)² − 3 (7) 64 − 3 (7) Multiply and divide in order from left to right. 64 − 3 (7) 64 − 21 Add and subtract in order from left to right. 64 − 2143

Turn right: (3 ÷ 5 ) (-12 x -5) − (4² + 1)

 Complete operations within parentheses. (3 ÷ 5 ) (-12 x -5) − (4² + 1) ( x ) (+60) − (16 + 1) () (60) − 17 Multiply and divide in order from left to right. () (60) − 17 40 − 17 Add and subtract in order from left to right. 40 − 1723

Turn left: -4 (-3 − 4.5) + (1.25 + 1.75)

 Complete operations within parentheses. -4 (-3 − 4.5) + (1.25 + 1.75)-4 (-7.5) + (3) Multiply and divide in order from left to right. -4 (-7.5) + (3) 30 + (3) Add and subtract in order from left to right. 33

The combination for page 3 is:

Left 43
Right 23
Left 33

43 + 23 + 33 = 99

### Summary

Match the clues to the owner:

• All the numbers in Isabella's combination are perfect squares. All the numbers on page 2 are perfect squares. Page 2 is Isabella's combination.
• Only 1 number in Jackson's lock combination is odd. Two of the numbers on Page 1 are even and only one of them is odd. (All the numbers on Page 3 are odd.) Page 1 is the combination to Jackson's lock.
• The remaining combination,on Page 3, must belong to Sebastian.

To check the combinations, add the totals:

Page 1 Page 2 Page 3
Left 42
Right 37
Left 20
Left 25
Right 49
Left 9
Right 16
Left 43
Right 23
Left 33
Total 99 Total 99 Total 99