Recitation 6 Well, if he makes 19 more jumps, he will land 2 pebbles away from his original position in the counter-clockwise direction. Another 19 jumps will lead him 3 pebbles away, and so on. After a total of 49 sets of 19 jumps, he will be 49 pebbles away from its original position in the counter-clockwise direction, which is of course the worms pebble. Then, the frog will have made 49* 19=931 jumps Here is the table produced by the Pulverizer: r rem 21 50-2.21 21 5=21-2.8 21-2·(50-2·21) 2·50+5.21 8-1.5 (50-2·21)-1·(-2.50+5·21) +5·21)-1·(3·50-7·21) 5·50+12.21 3-1·2 (3·50-7·21)-1.(-5:50+12.21) 8·50-19.21Recitation 6 4 Well, if he makes 19 more jumps, he will land 2 pebbles away from his original position in the counter­clockwise direction. Another 19 jumps will lead him 3 pebbles away, and so on. After a total of 49 sets of 19 jumps, he will be 49 pebbles away from its original position in the counter­clockwise direction, which is of course the worm’s pebble. Then, the frog will have made 49 ∗ 19 = 931 jumps. Here is the table produced by the Pulverizer: x y (x rem y) = x − q · y 50 21 8 = 50 − 2 · 21 21 8 5 = 21 − 2 · 8 = 21 − 2 · (50 − 2 · 21) = −2 · 50 + 5 · 21 8 5 3 = 8 − 1 · 5 = (50 − 2 · 21) − 1 · (−2 · 50 + 5 · 21) = 3 · 50 − 7 · 21 5 3 2 = 5 − 1 · 3 = (−2 · 50 + 5 · 21) − 1 · (3 · 50 − 7 · 21) = −5 · 50 + 12 · 21 3 2 1 = 3 − 1 · 2 = (3 · 50 − 7 · 21) − 1 · (−5 · 50 + 12 · 21) = 8 · 50 − 19 · 21 2 1 0