Push the Button!
From the Super Mario Wiki, the Mario encyclopedia
Push the Button! is a minigame found in Mario & Sonic at the Olympic Winter Games. To gain access to it, the player has to get Amy Rose to join their team. In Frostown, Mario and company will find a closed gate, with a totem full of character emblems near it. Amy can push the button on its top. However, she has to get rid of the four layers of the totem to reach the button. The player has to hit specific emblems in a specific order. They can find out which pictures to hit by talking to the Shy Guy, Toad, and the Chaos near it, though the Shy Guy lies to the player.
To win the game, the player must simply push the / button at the right timing and hit the correct emblem. If Amy hits the wrong one, she'll have to restart again. When all four layers of the totem are down, Amy must simply activate the button with her Piko-Piko hammer.
Hit the right marks to remove layers and reach the button! Mess up, and you start over!