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Puzzle for Today

Puzzle No. 239 – Friday 1 June

As it's World Milk Day, raise a glass of milk to celebrate this dairy themed puzzle! Old McDonald had a farm, and on that farm he had a special cow called EIEIO who was renowned across the lands for her milk yields.

An evil rival farmer released 11 other robot cows that looked identical in every way to Old McDonald's prized cow EIEIO. These 11 robot cows all weighed the same. However the cow EIEIO weighs either slightly more or less than the 11 robot cows.

Old McDonald needs to work out which is his prized cow EIEIO. He has a set of cow balance scales that can either tell him if the scales are equal, or whether one side is heavier than the other. There is a catch however: he only has 3 chances to weigh the cows in any combination using the scales to find the prized cow EIEIO. How would he do it?

Today’s #PuzzleForToday has been set by Bobby Seagull, a school Maths teacher and Cambridge University Doctorate student. He is co-author of the Monkman & Seagull Quiz Book.

Click here for the answer

There may be multiple solutions but here is one. Number the cows 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Put them into 3 groups : A(1,2,3,4), B(5,6,7,8) and C(9,10,11,12). Weigh group A and B. There are 3 possible outcomes:

Scenario 1: If they balance then group C has the prized cow, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:

1A) If 6,7,8 vs 9,10,11 balances, 12 is the prized cow. Weigh it against any other cow to determine if heavy or light.

1B) If 9,10,11 is heavy then they contain a heavy cow. Weigh 9 vs 10, if balanced then 11 is the odd heavy cow, else the heavier of 9 or 10 is the odd heavy cow.

1C) If 9,10,11 is light then they contain a light cow. Weigh 9 vs 10, if balanced then 11 is the odd light cow, else the lighter of 9 or 10 is the odd light cow.

Scenario 2: If group B > group A then either 5,6,7,8 contains a heavy cow or 1,2,3,4 contains a light cow so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:

2A) If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light cow or 7 or 8 is the odd heavy cow. Weigh 7 vs 8, if they balance then 4 is the odd light cow, or the heaviest of 7 vs 8 is the odd heavy cow.

2B) If 3,6,12 is heavy then either 6 is the odd heavy cow or 1 or 2 is the odd light cow. Weigh 1 vs 2, if balanced then 6 is the odd heavy cow, or the lightest of 1 vs 2 is the odd light cow.

2C) If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other cow, if balanced then 5 is the odd heavy cow else 3 is the odd light cow.

Scenario 3: If group A > group B then either 1,2,3,4 contains a heavy cow or 5,6,7,8 contains a light cow so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:

3A) If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light cow or 3 or 4 is the odd heavy cow. Weigh 3 vs 4, if they balance then 8 is the odd light cow, or the heaviest of 3 vs 4 is the odd heavy cow.

3B) If 7,2,12 is heavy then either 2 is the odd heavy cow or 5 or 6 is the odd light cow. Weigh 5 vs 6, if balanced then 2 is the odd heavy cow, or the lightest of 5 vs 6 is the odd light cow.

3C) If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other cow, if balanced then 1 is the odd heavy cow else 7 is the odd light cow.

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