You want a game that uses your dog's nose without scattering food every day. Their favorite toy is right there. Hide it behind the sofa while they are in another room, say "find it," and they stare at you. The problem may be that they have not yet learned the rules. Begin where the answer is easy to find.
Blue Cross describes scent-work games with both food and toys. Dogs use their noses naturally, but they still need to learn what your cue means and how the game ends. Make the first search obvious enough that the dog can succeed, then change only one thing at a time.
Make the first hide visible
Choose a toy your dog enjoys and a room without clutter or unsafe objects. Show the toy, place it a few feet away where they can see it and invite them to get it. When they approach or pick it up, celebrate in a way your dog likes: a short game, praise or an appropriate treat. Repeat a few easy placements. If they are not interested in the toy, choose a different one, the game should be rewarding from the dog's point of view.
Next, put the toy partly behind a chair leg while the dog watches. Then hide it around a corner but within a short search. Give them time to sniff. If they look lost, make the toy more visible or guide them toward the area. You are not testing whether they can solve a puzzle with no help. After they find it, reset and end while they still want another turn.
Build distance and difficulty slowly
Only when those hides are easy should you ask the dog to wait in another room or have someone hold them while you hide the toy out of sight. Use a simple cue once, then let them search. Avoid repeating the cue over and over when they need a hint. You can move to a different safe room or hide the toy at a low reachable level. Do not put it where the dog must climb unstable furniture, tear a cushion or knock over a lamp to reach it.
A dog with mobility problems may enjoy a short floor-level search rather than a whole-house game. Puppies can have very brief sessions. If the dog becomes frustrated, returns to you repeatedly or begins chewing household items instead, make the hide easier and shorten the game.
Keep the toy safe
Supervise the game. If the dog chews off parts of the toy, remove it. Do not use small items they might swallow. If you have more than one dog and either guards toys, let them search separately with secure barriers rather than turning the game into a competition. A dog who suddenly stops wanting a formerly favorite toy may be uncomfortable or unwell, ask your vet about a significant behavior change.
Common mistakes
Hiding the toy too well on the first try makes the cue meaningless. Using the same cue for food, a lost household object and the toy without teaching each version can confuse the task. Praising only at the very end may miss a dog's useful first sniff toward the right place, help them see what works. And a game in a cluttered room can invite unsafe climbing or chewing.
Today, put the toy in plain sight a few feet away and make the find fun. Tomorrow, tuck one edge behind a chair leg. The pleasure of the game comes from the search, not from keeping the answer secret as long as possible. For more ways to use your dog's nose, see the sniffing and exploration guide, start with a toy they can find easily
Sources: Blue Cross, "Scent work for dogs": https://www.bluecross.org.uk/advice/dog/behaviour-and-training/scent-work-for-dogs . Dogs Trust, "Enrichment activities to keep your dog entertained": https://www.dogstrust.org.uk/dog-advice/life-with-your-dog/enrichment/enrichment-activities-for-dogs.