How to Solve Spot the Difference Puzzles: The Grid Method

To solve a spot the difference puzzle, stop searching at random and scan both pictures in the same fixed order, one small square at a time, ticking off each change as you find it against the stated total. Split the pictures into a grid, compare cell with cell, sort what you see into a few kinds of change, and recheck only the areas where your tally comes up short.

This guide gives the kinds of change to look for, a six-step grid method, a worked example with every change explained, quick tally tricks, and a practice puzzle with its answer.

What is a spot the difference puzzle?

It is a pair of pictures that look the same at first glance. One of them has been altered in a handful of places, and your task is to list every alteration. Many puzzles state how many changes there are, which turns a vague search into a count you can finish.

The pictures in this guide are made of tiles, so each change sits inside clear borders. The same habits work on a busy drawing of shelves, windows and tools. You just draw the grid in your head instead of on the page.

What kinds of change should you look for?

The changes you meet usually fall into one of a few groups. Knowing the list helps, because some kinds hide much better than others. The difficulty column below is our own rough guide, not a measured result.

Swaps and turns have one thing in common. Nothing leaves the picture and nothing new arrives, so a quick look at the whole scene may suggest that nothing has changed. A careful cell by cell look is the reliable way to catch them.

What is the step-by-step grid method?

1. Note the total and how it is counted. Write down how many changes the puzzle promises. That number tells you when to stop and when to keep looking. This guide counts changed tiles, so a swap counts as two; some puzzles count a swap as a single change, so check which rule yours uses.

1. Draw a grid. Split both pictures into the same small squares, for example six rows and six columns. Use pencil lines or fixed landmarks in your head.

1. Scan in reading order. Compare row 1, cell 1 in the left picture with row 1, cell 1 in the right one, then move along. Never jump ahead to something that catches your eye.

1. Compare one feature at a time. In each cell, ask in turn: is the same object there, is it the same shape, the same fill, the same size, facing the same way?

1. Mark every changed tile. Count each tile that is not the same in both panels once. Two tiles that swapped places are two changed tiles, even though one move caused both.

1. Check the tally. If your count is short of the total, rescan only the rows where you marked fewest. If it is over, look again at each mark and make sure the two tiles really differ.

How does the grid method work on a real example?

Here are two six by six tile panels. The symbols are a ring ○, a dot ●, a triangle △, a square □ and a diamond ◆, and a centred dot · marks an empty cell. Every tile that is not the same in both panels counts as one change, and the panels differ in exactly eight tiles. Try it before reading on.

Left panel

Right panel

Row 1. Cells 1 to 3 agree. In cell 4 the dot has become a ring. The shape is the same but the fill is gone, so this is a change of fill. That is changed tile one.

Row 2. Cells 1 to 4 agree. In cell 5 the square has become a diamond, a change of shape. That is changed tile two.

Row 3. Cell 1 agrees. Cell 2 held a square and now holds a triangle, and cell 3 held a triangle and now holds a square. The two tiles swapped places. One move, but both tiles now differ, so these are changed tiles three and four.

Row 4. Cells 1 to 5 agree. In cell 6 the dot is missing. That is changed tile five.

Rows 5 and 6. Cell 1 of row 5 held a dot, cell 2 held a diamond and cell 1 of row 6 held a ring. All three are now squares, three changes of shape. They touch side to side and form an L-shaped patch. These are changed tiles six, seven and eight.

The rest of rows 5 and 6 agree. The tally reads eight, which matches the stated total, so the search is complete.

Which quick tally tricks help?

A few counting tricks work well before or after the full scan.

The row tally. For each row, count how many of each symbol it holds in each panel. If the counts differ, that row certainly has a change. In the worked example this picks out rows 1, 2, 4, 5 and 6 at once.

The tally misses row 3, though. A swap moves tiles without adding or removing any, so the counts stay equal. That is the weakness of every tally: it can confirm a change is there, but it can never confirm a row is clean.

The column tally. Do the same down each column. The swap in row 3 moves a square into column 3 and a triangle into column 2, so both columns now show different counts. In the worked example the column tally marks every column, including columns 2 and 3 where the swap sits.

It has its own blind spot, though. A swap between two tiles in the same column keeps every column count equal, just as this swap keeps row 3 equal. Run both tallies, and treat neither as proof that an area is clean.

The halves check. Split the panels into a top half and a bottom half and note how many changes you have in each. In the example the top three rows hold four changed tiles and the bottom three hold four. A half with fewer changes than you would expect is the first place to rescan.

Why is finding what two pictures share so hard in general?

A much harder related problem comes from network mathematics. A network here means a set of points with links between some pairs of them. Two pictures can be described as two such networks, and their shared part is the largest network that fits inside both.

A paper published on 27 March 2023 opens by noting that this task, known as the maximum common subgraph problem, has long been proven NP-hard ^[1]. The same paper reports that methods for finding the common part have been published since the 1970s ^[1].

A spot the difference puzzle avoids that hard part. The two pictures are already lined up, so each cell of one panel pairs with the same cell of the other. You never have to work out which piece matches which. This contrast is our own comparison, not something the cited work says. What is left is patient checking, and a fixed scan order makes that checking hard to skip.

Does the order of comparison matter?

Some puzzles show more than two pictures and ask what all of them share, or which one stands apart. The order in which you compare them can change what you end up with.

The 2023 paper extends the shared-part question to many networks at once ^[1]. One simple plan compares the first two, keeps their shared part, and then compares that with the next one ^[1]. The paper gives an example of three networks where this plan, run in one order, ends with nothing in common, while the reverse order reaches the true two-point answer ^[1].

That plan, which the paper calls the waterfall approach, still came close ^[1]. On its own test set of network triples, the paper reports that it reached about 98.5% of the size of the exact answer on average, while a faster tree-shaped plan reached about 96.3% ^[1]. On sets of six networks the tree plan fell to about 65.4% ^[1].

Exact search on sets of more than two networks was far slower, and the approximate plans ran orders of magnitude faster in its tests, which used collections of networks rather than pictures ^[1].

The lesson for a puzzle with several pictures is our own. Pick a reference picture, compare each of the others with it directly, and keep separate notes. Building one shared list step by step can drop details you later need.

How should you box the changes you find?

Many puzzles ask you to circle or box each change. Picture the changed tiles as a grid of ones and zeros, a one for every changed tile. Each box is then a rectangle of ones, touching changed tiles may share a box, and a tidy answer uses as few boxes as possible.

Splitting the ones of such a grid into the fewest rectangles that do not overlap is a puzzle of its own. One paper on that splitting task builds part of its argument by cutting the shape along a carefully chosen straight segment that runs between two of its inward corners ^[2]. A cut of that kind either splits the shape into two pieces or leaves it in one piece with one hole fewer ^[2].

For the worked example you can find the answer by hand. Each lone changed tile needs one box, and the swapped pair fits in one box. The L-shaped patch is not a rectangle, so it needs two boxes. That makes six boxes for eight changed tiles, and listing every way to cover the patches shows that no smaller set of rectangles works.

A box and a changed tile are not the same thing, which is why the count asks for tiles, not boxes.

Which mistakes should you avoid?

• Stopping at an easy total. If the puzzle promises a number, keep going until the tally matches.

• Counting a swap once. Two tiles that traded places are two changed tiles. Count both.

• Trusting a quick glance. Swaps and turns keep every object on the page. Only a cell by cell check catches them.

• Reading the grid out of order. Jumping to whatever stands out leaves quiet cells unchecked.

• Ignoring empty space. An added object often sits in a plain area the eye skips.

Can you solve this practice puzzle?

Here are two more panels, using the same symbols plus a triangle turned upside down ▽. They differ in exactly seven tiles, again counting every tile that is not the same in both panels. Use the grid scan, then confirm with the row and column tallies.

Left panel

Right panel

Answer: seven tiles changed. The list below has six items because item 2 covers two tiles.

1. Row 1, cell 2: the triangle is turned upside down.
2. Row 2, cells 5 and 6: the triangle and the square swapped places, two changed tiles.
3. Row 3, cell 1: the triangle has become a diamond.
4. Row 4, cell 3: the ring is filled in and becomes a dot.
5. Row 5, cell 6: a diamond was added to an empty cell.
6. Row 6, cell 4: the square is missing.

Notice that the row tally misses the swap in row 2, just as before, and the column tally catches it. Comparing every cell of the two panels confirms that these seven tiles are the only ones that differ.

Ready for a real test of your scan? In this riddle, called Twin Panels, you must work out how many tiles were changed.