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### Prime Presents 1

Two days ago, Rachel bought some gifts, and each cost a prime number of dollars. When she wrote down all the prices, each digit from 1 to 9 was represented exactly once. The total bill was the minimum possible for this situation.

*What was the bill and how many gifts did she buy?*

### Prime Presents 2

Yesterday, Alex bought some gifts, and each cost a prime number of dollars. When he wrote down all the prices, each digit from 0 to 9 was represented exactly once. The total bill was the minimum possible for this situation.

*What was the bill and how many gifts did he buy?*

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## Solutions to week 112

For **Precise Prescription**, transfer water until the 5-ounce vial contains 4 ounces of water. Dissolve the tablet in this water. Measure out and discard 3 ounces of the mixture. Add 4 ounces of water to fill the 5-ounce vial. Measure out and discard 3 ounces of the resulting mixture. The required dose remains in the 5-ounce vial. In **Gift Dilemma**, the DVD set costs **$33**.

**Precise Prescription answer explained:** Notation: (A, B, f_{A}, f_{B}) indicates A ounces and f_{A} of a tablet in the 5-ounce vial and B ounces and f_{B} of a tablet in the 3-ounce vial. The first step always begins by filling one or other vial and proceeds in sequence after each step. Putting in the tablet is counted as a step.

12 steps are needed. (5,0,0,0), (2,3,0,0), (2,0,0,0), (0,2,0,0), (5,2,0,0), (4,3,0,0), (4,0,0,0), (4,0,1,0), (1,3,.25,.75), (1,0,.25,0), (5,0,.25,0), (2,3,.1,.15). The dose is now in the 5-ounce vial.

## Recent Weeks

**Week 112**: Precise Prescription & Gift Dilemma, solutions to Pumpkin Crop & The Halloween Goblin

**Week 111**: Pumpkin Crop & The Halloween Goblin, solutions to Making 25 & Two Ways to 32

**Week 110**: Making 25 & Two Ways to 32, solutions to Commuters’ Dilemma & Construction Conundrum

**Week 109**: Commuters’ Dilemma & Construction Conundrum, solutions to Nine Coins & Five Questionable Coins

**Week 108**: Nine Coins & Five Questionable Coins, solutions to Ten from Two & Triangular Boundary

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

**Come back next week** for answers and more puzzles.