Skip to content
puzzles

Archive

Chain for

medium4 moves

The board

TargetTarget: 386
Running value: 41
  1. 41

0 of 4 moves

Reach the target in exactly 4 moves. Nothing here is recorded — this day is over.

Show the solution
  1. 41 → 133: +92: 41 → 133
  2. 133 → 173: +40: 133 → 173
  3. 173 → 371: swap digits: 173 → 371
  4. 371 → 386: +15: 371 → 386

Today's chain starts at 41 and has to finish on 386 in exactly 4 moves, each tile used once.

The hand: +15, swap digits, +92, +40, +14. +15 moves you up by 15; from 41 that is 56. swap digits turns 41 into 14 straight away, and it changes digit count when a number ends in 0. +92 moves you up by 92; from 41 that is 133. +40 moves you up by 40; from 41 that is 81. +14 moves you up by 14; from 41 that is 55.

First, +92: 41 → 133. This is the move that crosses 100. Then +40: 133 becomes 173. That leaves 213 still to gain. swap digits next, taking 173 to 371. That leaves 15 still to gain. +15 next, taking 371 to 386. It lands exactly on 386.

Working backwards helps: the chain can finish on +40 or +15; take +15, which turns into 386 from 371. So the real question is how to reach 371 in 3 moves from 41 with the remaining tiles.

Step by step, the choices narrow: At 41, 5 tiles are legal and 2 of them still lead to 386. At 133, 4 tiles are legal and 2 of them still lead to 386. At 173, 3 tiles are legal and 1 of them still leads to 386. At 371, 2 tiles are legal and 1 of them still leads to 386.

Why not +14? Put it in for +15 and the chain ends on 385, 1 below the target — a near miss, but a miss.

In total there are 4 ways to land within 10 of 386 without hitting it, and 4 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.

How Chain works

You start on one number and have to end on the target, using each tile in the hand at most once, in whatever order you like. Tiles add, subtract, multiply, divide — division only when it comes out exact — or swap the digits of the running value. The number of moves is fixed: it is the length of the shortest solution, so playing fewer never ends on the target and there is no longer route to take. A chain that uses all its moves and misses counts as a try, and the board goes back to the start; undo and reset are free. Exactly one set of tiles works, and the rest are there to look plausible.

The full rules, with worked examples · how to find the set faster

Share this day: https://puzzles.softaleo.com/archive/2026-09-13

    Chain for Sunday 13 September · puzzles