MYTS 2018 - Grade 5 - Round 2

A robot moves at 1 metre per minute. It goes straight for 2 minutes, turns left at a right angle and goes 3 minutes, turns right and goes 2 minutes, turns right and goes 5 minutes, turns left and goes 3 minutes, then turns left and goes 2 minutes. Draw its path and find the distance between its start and finish.

Rectangle ABCD has area 100 cm² and the equally spaced side marks shown. Find the total area of the shaded triangles.

Find all two-digit numbers divisible by 4 for which twice the number plus 3 is divisible by 5.

Two containers I,II hold water. First pour 1/3 of the water in I into II, then pour 10 litres from II back into I. The amount in I is now twice that in II. How many litres were initially in II?

Four football teams M,Y,T,S play a single round robin. A win gives 3 points, a draw 1 and a loss 0. M finishes with at least as many points as T. T’s total goals for and against are 4–1; M’s are 1–4. What scores occurred in M’s three matches and in T’s three matches?

Dương has three pebble piles initially containing 10,20,60 pebbles. Each move takes one pebble from each of two piles and puts both into the remaining pile. (a) After 10 moves, the destination piles have been pile 1 three times, pile 2 four times, pile 3 three times. How many pebbles are in each? (b) Can any finite sequence make the three piles equal? Explain.