First let me tell you something about the word ARE that you can astound your friends with. As you can see it has only one syllable. But did you know it becomes three syllables by adding just one letter to it? Cool, no? Trouble is you have to figure it out first though.

Now, imagine that a 4x4x4 inch cube is perfectly sliced so that when the pieces are separated they are all in the form of 1x1x1 inch cubes. Ziggurat-like (look it up) structures can then be formed with the remaining cubes. The smallest of such structures would have 1 cube centred on the top of a square layer of 4 cubes. Other structures can also be made but are only considered ziggurat-like if each layer is in a square formation, perfectly centred upon the layer below it (except for the bottom layer), smaller than the layer below it (excepting the bottom layer), and has a 1 cube pinnacle for the top layer. How many different ziggurat-like structures can be formed from the available cubes, assuming that all of the cubes can be used for building each structure?

Throughput

(The burnt out problem was: “The nonsensical sentence that follows conceals an important form of communication and artistic expression. See if you can find out what it is: NOW YOU’RE SEEING TRUE MIRING CONUNDRUMS GLIMMER.”)

The answer is WRITING, taking the last letter of the first word, then the last but the first letter of the second word, then the last but the second letter of the third word and so on.

No credit claimed as answer lifted from Google! -- J Vaseekhar Manuel, orcontactme@gmail.com

Other words that could be constructed using letters from the given sentence, like SIGNS, DRUMS, DRUMMING, LECTURE, that to some extent agreed with the clue also seemed possible candidates. Only when I wrote the words in the given sentence one below the other I could see the WRITING in the clue (pun intended). -- Balagopalan Nair. K, balagopalannair@gmail.com

(The second one was about the hiker from way back when which no one had got so I thought of putting in my own two cents worth.)

Always replenishing his supplies from available caches as soon as possible on outward trips, and taking just enough food for each cache on return trips to last until the next cache, the hiker can leave 3 days’ food 1 day into the desert -- denoted as (3,1) -- then continue (3,2). (3,1), (1,4), (3,1), (3,2), (3,3),(3,1), (3,5). Then without replenishing supplies do (1,2). Now the hiker can start with day’s food in his pack and pick up 2 day’s worth after 1 day’s walk, then 1 day caches at the end of days 2, 3, 4 and 5. Now with his pack full of food, he can finish the trip in 54 days. -- Dhruv Narayan, dhruv510@gmail.com

(The third problem was: “What number continues the following series: 4, 5, 35, 56, 83, ?” The hint given was “Mensa”.)

The word Mensa meant it was an ultra tough challenge. Out of curiosity, went into mensa.org. It also refers to a table. The first thing that came to my mind was the periodic table. After downloading all the elements with various details in a spreadsheet, I set about finding the relationship of elements with the numbers given by sorting on name, atomic number and position in the periodic table. There it was. The sequence represented atomic numbers of all elements that start with B in ascending order. The next two numbers are 97 and 107 corresponding to Berkelium and Bohrium. -- Saishankar Swaminathan, saishankar482@gmail.com

The next number in the series is 97. The series is, in ascending order, of the atomic number of elements in the Periodic Table which begin with the letter ‘B’. The hint of course was Mensa, which means Table! -- Charanjit Singh Pardesi, cspardesi@gmail.com

But Google This Now

1. A, B, C and D have to cross a bridge at night. The bridge can hold at most two persons at a time and each crossing must take place with a lit candle which burns for only 17 minutes. A, B, C and D take 1, 2, 5 and 10 minutes respectively to cross. Any two persons must walk at the rate of the slower person. The candle can’t be cut or thrown across. So how?

2. What emotion is an anagram of a homonym of an antonym of a homonym of an anagram of WOLF?

Sharma is a scriptwriter and former editor of Science Today magazine.

**Mukul Sharma**

**(mukul.mindsport@gmail.com)**