## ________________

Spring is in the air, so the coach provides a baseball puzzle and a swimming puzzle.

## ________________

### Batting Order

The players in the initial lineup of the Sluggers have jerseys numbered 1 to 9. Players in even-numbered batting positions have even-numbered jerseys, and each player’s jersey number is different from his or her batting order position. Players next to each other in the batting order have jersey numbers that differ by more than one. The Sluggers’ opponents have the same situation but a different batting order.

*What are the batting orders of the two teams?*

### Swimming Workout

Team member Randall says, “I swam from our campsite this morning straight across the lake at my normal constant rate to the mouth of a stream flowing into the lake. I then swam upstream for a while to a lovely spot, took an hour for lunch, swam back downstream to the lake and straight back to our campsite at my normal rate. My total time away was exactly 3 1/2 hours.”

Sophie asks, “How far did you swim?”

“I don’t know any of the distances involved,” answers Randall, “but I do know my average speed downstream relative to land was 1.2 miles an hour and my average speed upstream relative to land was 0.6 miles an hour.”

Sophie says, “Since I know your normal swimming speed, that’s all I need to know.”

*How far did Randall swim and how fast does he swim in the lake?*

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## Solutions to week 134

To solve Maximization, let a = .1^{-4} = 10000 and b = .2^{-a} = 5^{10000}. Then **M = .3 ^{-b}** is the maximum. For the answer to Multiplication Table see the diagram below.

**Maximization answer explained:**

Let a = .1^{-4} = 10000 and b = .2^{-a} = 5^{10000}. Then M = .3^{-b} is the maximum. Ln(ln(M)) ≈ 16095. Ln(x) is the natural logarithm of x.

## Recent Weeks

**Week 134**: Maximization & Multiplication Table, solutions to Maximizing Links & Seven Points

**Week 133**: Maximizing Links & Seven Points, solutions to Time of Day & The Missing Element

**Week 132**: Time of Day & The Missing Element, solutions to Knight Trap & My Number is 136

**Week 131**: Knight Trap & My Number is 136, solutions to The Size of Humanity & Fish Pond

**Week 130**: The Size of Humanity & Fish Pond, solutions to Circumnavigation & Typos

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

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