- 59 → 93: +34: 59 → 93
- 93 → 56: −37: 93 → 56
- 56 → 149: +93: 56 → 149
- 149 → 298: ×2: 149 → 298
From 59 to 298: 4 moves, no tile twice, and only one set of tiles gets there.
The hand: +43, ×2, +93, +34, −37. +43 moves you up by 43; from 59 that is 102. ×2 multiplies by 2 — an even number, so it can never land on an odd target directly; 298 is a multiple of 2. +93 moves you up by 93; from 59 that is 152. +34 moves you up by 34; from 59 that is 93. −37 takes 37 off; from 59 that is 22.
First, +34: 59 → 93. That leaves 205 still to gain. Move 2: −37, 93 → 56. That leaves 242 still to gain. Then +93: 56 becomes 149. That leaves 149 still to gain. ×2 next, taking 149 to 298. 298 is even, as any ×2 result must be.
Working backwards helps: the final move must be ×2, because 149 is the only value in reach that turns into 298. So the real question is how to reach 149 in 3 moves from 59 with the remaining tiles.
Step by step, the choices narrow: At 59, 5 tiles are legal and 3 of them still lead to 298. At 93, 4 tiles are legal and 2 of them still lead to 298. At 56, 3 tiles are legal and 1 of them still leads to 298. At 149, 2 tiles are legal and 1 of them still leads to 298.
Why not +43? Play ×2, +43, +93, +34 and the chain ends on 288, 10 below the target — a near miss, but a miss.
In total there are 8 ways to land within 10 of 298 without hitting it, and 6 orders of the right tiles that do hit it.
Once the set of tiles is right, the order usually follows from what is legal at each step.