Like Denominators
5/9 + 2/9
3/9 = 1/3
2/3 - 1/6
1/2
You have 3 boxes: one with apples, one with oranges, one mixed. Labels are all wrong. You can open one box and take one fruit. How do you know all labels?
Open the “mixed” box — since labels are wrong, it contains only one type. That tells you how to fix all labels.
4/11 + 6/11
10/11
3/5 + 1/10
7/10
You have 8 balls, one heavier. How can you find it using only 2 weighings?
Split into 3–3–2. Weigh 3 vs 3. If equal → heavier in group of 2. If not → heavier in group of 3, weigh 1 vs 1.
7/12 - 5/12
2/12 = 1/6
7/8 - 1/2
3/8
There are 3 switches outside a room. One turns on a lamp inside. You can enter the room only once. How do you find the right switch?
Turn on switch 1 for a minute, then off. Turn on switch 2. Enter: lamp on → switch 2; lamp off but warm → switch 1; lamp off and cold → switch 3.
9/15 + 3/15 - 5/15
7/15
5/12 + 3/8
19/24
A farmer must take a wolf, a goat, and a cabbage across a river. The boat can carry only one at a time. If left alone, the wolf eats the goat, the goat eats the cabbage. How can he do it?
Take goat first. Return alone. Take wolf, bring goat back. Take cabbage. Return alone. Finally take goat. All safe.
2/7 + 3/7
5/7
1/2 + 1/4
3/4
You have two ropes. Each burns in 1 hour, but not evenly. How can you measure 45 minutes?
Burn rope 1 from both ends and rope 2 from one end. Rope 1 burns in 30 minutes. Then light rope 2 from the other end → burns in 15 minutes. Total = 45 minutes.