- 79 → 133: +54: 79 → 133
- 133 → 188: +55: 133 → 188
- 188 → 160: −28: 188 → 160
A short chain today — 3 moves from 79 to 160 — but the hand holds more tiles than you need.
The hand: +65, −28, +55, +54, −36. +65 moves you up by 65; from 79 that is 144. −28 takes 28 off; from 79 that is 51. +55 moves you up by 55; from 79 that is 134. +54 moves you up by 54; from 79 that is 133. −36 takes 36 off; from 79 that is 43.
Working backwards helps: the chain can finish on +54 or +55 or −28; take −28, which turns into 160 from 188. So the real question is how to reach 188 in 2 moves from 79 with the remaining tiles.
First, +54: 79 → 133. This is the move that crosses 100. +55 next, taking 133 to 188. That is 28 above the target, to be brought down. Then −28: 188 becomes 160. It lands exactly on 160.
Step by step, the choices narrow: At 79, 5 tiles are legal and 3 of them still lead to 160. At 133, 4 tiles are legal and 2 of them still lead to 160. At 188, 3 tiles are legal and 1 of them still leads to 160.
Why not +65? Put it in for +55 and the chain ends on 170, 10 above the target — a near miss, but a miss. Why not −36? Put it in for −28 and the chain ends on 152, 8 below the target — a near miss, but a miss.
In total there are 24 ways to land within 10 of 160 without hitting it, and 6 orders of the right tiles that do hit it.
That is the whole solution; every other combination of tiles ends somewhere else.
A last check that costs nothing: 160 ends in 0, is even, and divides by 2, divides by 5; the start, 79, ends in 9. Those two facts rule out most tile sets before you touch the board, which is the whole trick of Chain.