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Did you solve it? Are you craftier than a cat burglar?
Did you solve it? Are you craftier than a cat burglar?

The Guardian

time12-05-2025

  • General
  • The Guardian

Did you solve it? Are you craftier than a cat burglar?

Earlier today I set these two puzzles. Here they are again with solutions. 1. Go compare! A dealer places one hundred cards on a table. On their face-down sides are the numbers from 1 to 100. The cards are randomly arranged so you have no idea at the beginning which card is which. Your task is to identify the 1 card and the 100 card without turning any of them over. The only way to learn information about the cards is by comparison. At any stage, you may choose two and ask the dealer which is smaller and which is larger. The dealer always knows. They will never tell you the number on the cards, just which is smaller and which is larger. It is possible to identify the 1 card after asking the dealer to make 99 comparisons. First, ask them to compare any two cards. Make a note of the lower card, and ask them to compare it with one of the 98 remaining cards. Make a note of the lower card, and ask them to compare it with one of the 97 remaining cards. And so on. The lower card in the 99th comparison must be lower than all other cards, and thus is the 1 card. Likewise you can identify the 100 card after 99 comparisons, making a total of 198 comparisons to find both highest and lowest cards. Can you find a method to identify the 1 and the 100 cards using less comparisons? What's the optimal strategy? Solution You can do it in 148 comparisons. STEP 1: Divide the cards into fifty pairs. Ask the dealer to compare the cards in each pair. (Total: 50 comparisons.) STEP 2: Consider the 50 lower cards from these comparisons. This group contains the 1 card. It will take 49 comparisons to identify with 100 per cent certainty which is the 1 card, which we do by comparing any two cards, taking the lower one, etc, and going through the remaining 48 as we did above. STEP 3. By the same logic, the remaining 50 cards contain the 100 card. It will take 49 comparisons of this group to identify with 100 per cent certainty the 100 card. TOTAL: 50 + 49 + 49 = 148 comparisons. This strategy is optimal. The proof is somewhat technical for a general audience, but if any mathematicians want to write it down in full in the comments below I'm sure some readers will be grateful. 2. The rope trick You are a burglar at the top of a 20m building, which has a ledge half way down on which it is possible to stand. There are hooks at the top of the building and on the ledge. You have a 15m length of rope and a knife. You can cut the rope if you like, and also make any type of knot anywhere on the rope, which uses up no length, and which can be placed on either hook. How would you use the rope to descend the building safely? You are not allowed to jump off the building or the rope. Solution Cut the rope into two pieces of 5m and 10m. Make a knot at one end of the 5m rope. Thread the 10m rope through this knot and tie its ends together. Make a knot at the other end of the 5m rope and attach it to the hook. Dangle the ropes down the side of the building and climb down them. The joined ropes have a combined lenth of 10m (5m + 5m), which gets you to the ledge. Untie the ends of the 10m rope and pull it through the other rope. This rope will get you down the final 10m when you attach it to the hook on the ledge. Thanks to Geza Bohus for suggesting today's puzzles. Geza was a Hungarian maths olympiad contestant many moons ago and is now semi-retired after a career in academia and industry, specialising in machine learning and financial modelling. These are two of his favourite puzzles. I've been setting a puzzle here on alternate Mondays since 2015. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.

The 1% Club knocks out 17 players with simple picture question – but would you get it in 30 seconds?
The 1% Club knocks out 17 players with simple picture question – but would you get it in 30 seconds?

The Sun

time12-05-2025

  • Entertainment
  • The Sun

The 1% Club knocks out 17 players with simple picture question – but would you get it in 30 seconds?

A PICTURE round on The 1% Club wiped out a whopping 17 players - yet would you have guessed it in the 30-second time frame? Saturday's episode of Lee Mack 's ITV game show - which has taken the nation by storm - left many flustered with what appeared to be a relatively easy round. 6 6 6 6 The 1% Club is a unique format that doesn't test players on their general knowledge like other shows. Instead, it tests them on their logic, reasoning skills and common sense. 100 players are whittled down, question by question, as they are tasked with solving different riddles. They aim to get to the last round where only one percent of the public could answer the final question correctly. On Saturday, show anchor Lee - who was recently slammed by fans after a personal comment to one player on-air - told the players: "Right we are at the 25 per cent stage now. "In this puzzle, where are you going?" An image flashed up on screen of the word round, surrounded by circles in different colours. After the time was up, he told how the answer was: "Round in circles." Out of the 17 contestants wiped out, one was Harvey. He told Lee how he had put "round the centre" instead, before being eliminated from the game. The 1% Club players struggle through 'suspiciously easy' 80k question - could you have got it right in 30 seconds- Yet those watching at home took the opposite stance. They branded the episode "easy" with one posting on X: "Another abysmally easy episode of #The1PercentClub." Another put: "That 5% question was really easy - more like a 90% question." A third noted: "Blimey. That's three weeks running I've got the final question correct." The 1% Club's Most Difficult Questions The 1% Club sees 100 contestants try and make it to the 1% question and be in with a chance to win a share of the jackpot. Here are just some of the show's most difficult teasers. Players had to compare and contrast three images of butterflies then explain which of the butterflies were exactly the same on both sides. Find the image and answer here. Players were shown groups of six symbols then asked which were in the same order whether you read them from left to right or right to left. Find the image and answer here. Players were asked how many different combinations were there of displaying four digits on one hand. Find the answer here. Peter had recently found his old diary that he'd written in secret code but he couldn't remember how to decipher what he wrote. Players were asked to crack the code and find out what the bold word was. WH89 I GR1W UP I WA92 21 B8 A 5L1RI72. Find the image and answer here. Players were tasked with working out how many eyes they could see in an image, which was made up of letters, symbols and emojis. Find the image and the answer here. A 1% question was based on a grid of numbers going in ascending order from 1 to 49. Starting on 25, the middle square, SEEN took you to square 27. From there, NEW took you to 20. From there, which square would SEWN take you to? Find the image and the answer here. And finally, an easy one - What common food in bold has had its letters rearranged into alphabetical order? ABDER If you really don't know you can find the answer here. The show wrapped with contestant Marc scooping the 94K prize. Previously, a swathe of competitors were knocked out by a very "easy" question. A picture of a cat also posed issues for some brainboxes. 6 6

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