On December 30, 2025, British mathematician Neil Saunders released 10 math problems just before Christmas, challenging people’s thinking skills. Now, he has unveiled the answers and explanations to these questions. Let’s take a look at how many you got right:
(1) Solution with only two weighings:
– First, divide 9 coins into 3 groups of 3 coins each, then weigh two of the groups. If one group is lighter than the other, the counterfeit coin is in that group. If the weights are the same, the counterfeit coin is in the unweighed group.
– Take out the group with the counterfeit coin, then weigh 2 coins. If one is lighter, it’s the fake coin. If they weigh the same, the counterfeit is the third coin.
(2) A solution for baking a pie quickly involves setting two timers simultaneously and precise steps following the timers’ durations for perfect baking.
(3) An 11-step solution involving pouring wine back and forth between two buckets to measure specific volumes with 10 and 5-liter buckets.
Moving on to the calculations:
Setting s as the sum of the first 100 numbers, we can write: s = 1 + 2 + 3 + 4 + … + 99 + 100. By reversing the order, s = 100 + 99 + 98 + … + 4 + 3 + 2 + 1. Adding these two equations, we get 2s = 10,100, thus s = 5,050, representing the total amount you receive, which is £5,050.
(5) The sequence represents the number of letters in the gifts received each day in the Christmas carol “The Twelve Days of Christmas.” For example, 5 represents the swans, and the complete gift list is listed with the corresponding letter count.
(6) Among 100 statements, only the 99th statement is correct, stating the exact number of incorrect statements in the list, setting an interesting logic puzzle.
(7) Deduction of the color of your hat based on the statements and deductions made by Arthur and Bob regarding the colors of their hats, showcasing a logical reasoning puzzle.
(8) A logic puzzle involving mislabeled boxes and the process of deducing the correct labels through the observation of the contents of the boxes.
(9) A demonstration of invariance, showcasing how the liquid volumes in the juice bottles remain constant even after mixing and pouring, highlighting a mathematical principle.
(10) A trick involving Christmas-themed banknotes and statements to deduce the authenticity of the statements made by the elves, challenging the reader with a logical reasoning puzzle.
These thought-provoking puzzles and solutions shared by Neil Saunders provide an enjoyable exercise for those looking to test their problem-solving skills and logic abilities.