Earlier this week, one of our secondary school students astonished me by recalling a riddle I had put to him almost two years ago. “Did you know, sir?” he asked me, “that I can still remember you telling us about the case of the missing Euro. And I am still baffled by it.” “Really?” I replied, clearly picturing the conversation we had enjoyed together, but not completely certain of the circumstances. NB. A friendly caution: the story I am about to recount is long to hear and even longer to read!
Once upon a time, the riddle begins, a group of three Paris St. Germain (PSG) soccer fans happened to be in the wonderful city of Lyon to attend a match between their team and the local favorite, the Olympique Lyonnais (OL). Unfortunately for the PSG supporters, while their team had won the match 3-0 (sorry OL fans, having spent a large part of my life in St. Germain-en-Laye I could not resist), they missed their high-speed train home and needed to find a hotel where they could spend the night. Wandering around the area next to the OL stadium, the three friends soon found what looked like a charming place to stay.
When they entered the hotel, there were delighted by what they saw: a large sign indicating the very reasonable price of 10 Euros per night for a single room. So our three PSG fans headed towards the welcome counter, already digging into their pockets for the money they would need. “Good evening, gentlemen,” the hotel clerk greeted them. “Sincere congratulations to you on your team’s victory. It was much deserved (!). We do hope you’ll decide to reside in our hotel tonight and are happy to say we have three single rooms available for you, all on the same floor.”
“That’d be perfect. Thank you.” said the first friend, continuing, “I hope you won’t mind, but I’m afraid the three of us will only be able to pay for our stay with single Euro coins. We’ve had such a great time in Lyon that we’ve spent all of our bills and only have change left.” “Not a problem at all, sir,” came the reply from the hotel clerk, who added, “we could use the coins.” And so without further ado, each of the three PSG supporters counted out exactly ten single Euro pieces and slid them one by one across the counter to the hotel clerk on the other side, who in turn counted them again, moved them to the cash register and handed each friend a key. Number 31 for the first, number 32 for the second and number 33 for the third. “Have a restful evening, sirs,” said the hotel clerk. And off to sleep the three friends went.
Yet no sooner had they disappeared than the hotel clerk realized something. “Oh dear,” he thought aloud. “I forgot to give them the discount they deserve. Today is the first Saturday of the month and each first Saturday of the month we give a five Euro discount for every three rooms rented. That means we owe these three gentlemen money.” He rang the counter bell and in less than a minute one of his colleagues had appeared, asking what help was needed. “Alas, I forgot to give our third-floor guests the three-room discount. Could you kindly take it up to them?” “With pleasure,” replied the second hotel employee. The hotel clerk then removed five single Euro pieces from among the 30 the cash register, carefully checking to ensure that he had precisely what he needed. Picking up these coins one by one, the second hotel employee then headed in the direction of the third floor.
On his way upstairs, however, it dawned on the man that giving back the coins involved would be difficult. After all, he had five pieces to return to three people, meaning that unless something changed one person would receive one fewer coin than his two friends. “Hmmm,” he pondered. “I have an idea. Every day on my way to work, I pass in front of a charitable organization. What I’ll do is give that organization two Euros, which I am confident would make our guests happy if they knew, and then give each of them one of the remaining three Euro pieces, which is their equal share of the discount, so that everyone wins in the end. ” And that is indeed what he did, knocking on the doors of rooms 31, 32 and 33, and giving back a single Euro to each guest with an explanation about the special Saturday discount. The PSG fans were happy and so was the hotel employee, bounding off to give away the two Euros he had left.
Consider for a moment the arithmetic involved thus far. Each guest had given exactly 10 Euros to the hotel clerk in exchange for a room, meaning that the hotel had collected 30 Euros in total. Yet each PSG fan had also received a Euro coin back, so that he had ended up paying only nine Euros for the evening. As a result, the three men together had actually paid the hotel the sum of 27 Euros. Nine Euros from each of the three men, adding up to a total of 27 Euros. At the same time, while the second employee had personally restituted one Euro to each of the PSG supporters, thus ensuring that they would each only pay nine Euros and together 27 Euros, nine times three making 27, he had also given two Euros to a charitable organization.
So here’s my question. If the three friends only ended up paying 27 Euros and two Euros were given away, the total number of coins in existence at the end of the evening was 29, no? 27 plus two, which equals 29. And yet we know for sure that when they arrived at the hotel in the first place the three PSG fans had definitely handed over 30 Euros. If 30 Euros were definitely exchanged at the start, i. e. 10 Euros multiplied by three guests, and yet only 29 remained in the end, i. e. the nine Euros each man paid plus the two Euros which had remained and therefore been donated, what could possibly have happened to the missing Euro?
You may be asking yourself why I have gone on at such length about this story today, dear readers, and rightly so, especially as I am not entirely sure this riddle works as well in writing as it does in oral form, when the teller gets to bring the listener back again and again to the plot, trying to prevent him or her from applying a different logic from the one being misleadingly pushed to the forefront. My motivation? To underline one of the most outstanding qualities of our students here at the Lycée Français de New York. Yes, as evidence of how wonderful they are, we proudly and passionately emphasize their stellar academic and extracurricular achievements. Yet that one of our students would remember this long, complicated narrative 18 months after hearing it sheds light on them in a different way too, revealing the deep curiosity they feel about everything and the genuine joy they find in learning. Missing Euro or no missing Euro, our students love to think!
PS. If you have any riddles you would be willing to send me, please kindly do so. I know some 1300 people who will appreciate them all!
About the Author :
Sean Lynch was Head of School at the Lycée Français de New York from 2011 to 2018, after having spent 15 years at another French bilingual school outside of Paris: the Lycée International de St. Germain-en-Laye. Holding both French and American nationalities, educated in France (Sciences Po Paris) and the United States (Yale), and as the proud husband of a French-American spouse and father of two French-American daughters, Sean Lynch has spent his entire professional and personal life at the junction between the languages, cultures and educational systems of France and the United States. In addition to being passionate about education, he loves everything related to the mountains, particularly the Parc National du Mercantour.