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: $negative one-third$ (^-46.3 − 28.7) + $twenty-four-eighths$ x $sixteen-fourths$

Complete operations within parentheses.	$negative one-third$ (^-46.3 − 28.7) + $twenty-four-eighths$ x $sixteen-fourths$ $negative one-third$ (^-75) + $twenty-four-eighths$ x $sixteen-fourths$
Multiply and divide in order from left to right.	25 + $twenty-four-eighths$ x $sixteen-fourths$ 25 + 3 x 4 25 + 12
Add and subtract in order from left to right.	25 + 12 37

Turn left: (9² − 1) x ( $negative one-half$ )²

Evaluate powers within parentheses. Complete operations within parentheses.	(9² − 1) x ( $negative one-half$ )² (81 − 1) x ( $negative one-half$ )² (80) x ( $negative one-half$ )²
Evaluate powers.	(80) x ( $negative one-half$ )² (80) x $one-fourth$
Multiply and divide in order from left to right.	(80) x $one-fourth$ 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: $one-fourth$ (27.8 + 8.2) + $one-third$ (^-6 x ^-8)

Complete operations within parentheses.	$one-fourth$ (27.8 + 8.2) + $one-third$ (^-6 x ^-8) $one-fourth$ (36) + $one-third$ (48)
Multiply and divide in order from left to right.	$one-fourth$ (36) + $one-third$ (48) 9 + $one-third$ (48)
Multiply and divide in order from left to right.	9 + $one-third$ (48) 9 + 16
Add and subtract in order from left to right.	9 + 16 25

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 − 7 9

Turn right: (15 ÷ $three-fifths$ ) − (3.4² − 2.56)

Evaluate powers within parentheses.	(15 ÷ $three-fifths$ ) − (3.4² − 2.56) (15 ÷ $three-fifths$ ) − (11.56 − 2.56)
Complete operations within parentheses.	(15 ÷ $three-fifths$ ) − (11.56 − 2.56) (15 x $five-thirds$ ) − (11.56 − 2.56) ( $seventy-five over three$ ) − (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 − 21 43

Turn right: (3 $one-half$ ÷ 5 $one-fourth$ ) (^-12 x ^-5) − (4² + 1)

Complete operations within parentheses.	(3 $one-half$ ÷ 5 $one-fourth$ ) (^-12 x ^-5) − (4² + 1) ( $seven-halves$ x $four over 21$ ) (⁺60) − (16 + 1) ( $two-thirds$ ) (60) − 17
Multiply and divide in order from left to right.	( $two-thirds$ ) (60) − 17 40 − 17
Add and subtract in order from left to right.	40 − 17 23

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