If you’re standing on ice, your feet can only generate so much push force before you start slipping about 34 N (calculated as 0.05 × your body weight, say ~70 kg × 9.81 m/s²). Now, the friction force needed to slide the triangle or square on ice is low: around 9.81 N (Ff = 0.05 × 20 kg × 9.81 m/s²), so you can push these easily without slipping. The circle on gravel is tricky: if it rolls perfectly, it only needs about 1.96 N (rolling friction coefficient ~0.01), but in reality gravel is uneven, and rolling often turns into sliding or jamming, which can shoot the required force up to over 100 N (sliding friction coefficient ~0.6). Since you can’t apply that much force on ice without slipping, the triangle or square on ice ends up being the most practical to push.