Problematics | A classic remix of old milk in new bottle

What is there more of, milk in the glass of water, or water in the bottle of milk? Try to keep it simple.

Even without counting the number of people who solved last week’s puzzles correctly, it’s quite apparent that the response has been very strong. As some of you have observed, the puzzles were easier than usual.

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This week’s puzzles, too, might be considered easy. One of them is based on a classic, which means that the puzzle and its solution are both out there on the Internet. So, let’s tweak it a bit. Decades ago, Martin Gardner discussed an expanded version, to which I have added my own embellishments. Although the puzzle is still easy, the solution to this version will not be available on the Internet.

#Puzzle 38.1

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#Puzzle 38.1

Take a bottle of capacity 1 litre, 90% of which is filled with milk, and a 250ml glass, 90% of which is filled with water. You want to add a tiny amount of milk to the water and observe the slight tinge of white. For that you use a tablespoon (tbsp) and a teaspoon (tsp), the former’s capacity being three times that of the latter.

Transfer one full tablespoon of milk to the glass of water, taking care not to spill a drop, because you won’t be able to solve this puzzle if you do. You note that the tinge acquired is barely observable, so you want to add a bit more milk.

You are worried, however, that the next transfer of milk might result in some liquid spilling out of the glass. To prevent that, you take 1tbsp of liquid from the glass and transfer it back to the milk bottle. Mix thoroughly.

Now that the bottle and the glass both have as much liquid as before, it’s safe to make the second transfer. You don’t want to exceed the targeted whiteness, so you use the teaspoon this time, transferring 1tsp from the bottle to the glass.

As a final step, you transfer 1tsp of liquid back from the glass to the bottle.

What is there more of, milk in the glass of water, or water in the bottle of milk? Try to keep it simple.

#Puzzle 38.2

In Puzzles to Puzzle You, the inimitable Shakuntala Devi notes that in the date 8.8.64, the product of the first two numbers equal the third. Although she meant 1964, let’s take it as 2064.

How many dates with this property can you find across the 21st century?

#Puzzle 37.1

#Puzzle 37.2  Hey Kabir,  This time the puzzles are relatively easy but interesting all the same.  ABACAD + FGH = FGABCA + HDA  ELEVEN + TWO = TWELVE + ONE  — Nipun Bamania, Mumbai Indeed, Nipun, the list below bears out your assertion that last week’s puzzles were easy.

Solved both puzzles: Pranav Sharma (Panchkula), Nipun Bamania (Mumbai), Dr G L Arora (Delhi), Kanwarjit Singh (Delhi), Bhuman Vij (DPS Faridabad), Abhishek Kumar (Jalandhar), Vinayak Tamani (Navi Mumbai), Alka Mehta (Noida), Mudit Singhal (Mumbai), Shivika Gupta (Delhi), Sunita & Naresh Dhillon (Gurgaon), Dhariyan Jain (Mumbai), Abdullah Jamil Ahmad (Delhi), Prachi Gupta (Delhi), Atharva Tandon (Delhi), Mansi Gupta (Mumbai), Mahesh Mundhra (Indirapuram), Jasleen Kaur (Delhi), Gaurav Gummaraju (Navi Mumbai), Vijay Kumar (Delhi), Akshay Bakhai (Mumbai), Gochu Dhirajbhai Patel (Mehsana), Mayobhav Pathak (Gurgaon), Geetnasha Gera (Faridabad), Trusha Sohoni (Mumbai), Amardeep Singh (Meerut), Sarika Gupta (Panchkula), Sanjay Gupta (Delhi), Shabbir Padhri (Surat), Sandeep Bhateja (Hoshiarpur), Ankur Tiwari (Pune), Anshul Kumar (Delhi), Meenu Jain (Delhi), Deepika Verma (Gurgaon), Prachita Singh (Delhi), Prateek Gang (Ghaziabad), Nathan Sequeira (Mumbai), Bhavya SK and Dr Vivek CK (Delhi), Srang Sule (Mumbai), Madhuri Patwardhan (Thane), Shishir Gupta (Indore), Sujatha Ramanan (Delhi), Deviprakash Seskaria (Navi Mumbai), Shrey Gujral (Delhi), Anay Gupta (Indirapuram), Chaudhary Sudhir Kumar & Chaudhary Lucky Singh Randhawa (Mohammadpur, Shakist), Sabornee Jana (Mumbai), Rajesh Bansal (Noida), Rahul Agarwal (Bay Area, California), Yuthika Berdhe, Shriyukta, Samia Azmi, Aashvi Singhla, Sunitha Nair, Meenakshi Gupta

Solved #Puzzle 37.1: Avni Nayak (Airoli), Archit Taneja (Delhi), Swati Tandon (Delhi), Shweta Naikar (Vasai), Ram Sharma (Sonipat), Rahul RB (Mumbai), Mansi Khurana (Pataudi), Dr Raj Kumar Sharma (Hindu College, Sonipat), Gautam Kumar (Delhi), Dr Amanpreet Kaur (Kapurthala), Amit Angle (Gurgaon), Sandeep Asthana (Noida), Ganga Kumar Sinha (Ghaziabad), Amar Lal Miglani (Mohali), Somak Ghosh (Greater Noida), Tosheeba Naidu (Delhi), Moh Aqueel (Hans Raj College, Delhi), Abhinav Sharma, Ritesh Bahety, Rahul Goswami

Solved #Puzzle 37.2: Vandana (Noida), Ritu Verma (Pune), Arvind Sharma (Delhi), Jawahar Lal Aggarwal (Vasundhara, Ghaziabad), Sridhi Chamoli (Delhi), Chiranjeev Khurana (Pataudi), Jaikumar Bhatia (Ulhasnagar, Thane), Puneet Vashistha, Sanaya Atal, Pulkit Kumar, Vidya Pai

Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com