# 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 + 12 37 |

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 + 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 − 716 − 7 |

Add and subtract in order from left to right. | 16 − 7 9 |

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 − 21 43 |

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 − 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 |