Brainwave Units

E4
The problem hanging off the end of this first paragraph can be solved in less than a yoctosecond by a Cray XK7 supercomp but that's not the pomp. The real point is: can you do it using nothing but the O2 guzzling stuff that weighs about 1,400 gm and dreams the world with your eyes?
I have a ten-digit number, which contains each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and is exactly divisible by 10. If you remove the digit in the units place, the remaining nine-digit number is exactly divisible by 9. Again, if you remove the digit in the units place, the remaining eight-digit number is exactly divisible by 8. This process can be continued as described above till all the numbers have been knocked off one by one. What's the number?

DEAR MS
(The older problem was to discover in which Shakespearean play, and where in it, do the words "Want My Baby" appear in an acrostic as if the bard was hiding a message to someone. - MS)

Got-My-Babe-Dept:
I was trying to unravel your giving away the hint. After wracking my brain and going through the names of all the bard's plays, I decided to look at The Comedy of Errors. There it is in Act 1, Scene 1. This drama opens in the palace of the Duke of Ephesus as he is giving audience to a Syracusan merchant Aegon.
- Saishankar Swaminathan, saishankar482@gmail.com

The answer to the Shakespearean play is The Comedy of Errors in line 145, Act 1, Scene 1.
- Niraj Nandish, nirajnandish@icloud.com

(The other problem was: "At sunrise, a monk climbs a hill to meditate. He walks at varying speeds, even stopping frequently. After some days, he comes down - starting again at sunrise - with varying speed along the same path. Can it be proven that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day?" - MS)

Traipsing-Monk-Dept:
It's a simple problem camouflaged with a large quantity of irrelevant information and a lot of red herrings. Let's assume that the two trips are undertaken on the same day by two monks, both simultaneously starting at sunrise, one going up and the other coming down at whatever rate they choose. They will inevitably cross each other at some point along the track. In other words, they will be at the same spot at precisely the same time of day.
- Balagopalan Nair, balagopalannair@gmail.com

(The third one was: "You're given a large bucket filled with water, a wooden ruler and a soccer ball. Determine, approximately, the diameter of the ball using only these items." - MS)

Drop-In-The-Bucket-Dept:
First, measure the radius of the top level of water with the scale. Then, immerse the ball fully in the water and measure the radius of the top level again, if the bucket is in the shape of a frustum; if it is cylindrical, then no need to measure the radius twice - just go ahead and measure the rise in water column. Now, according to Archimedes Principle, the volume rise in the water level will be equal to the volume of the ball submerged in water. Apply the formula for volume of sphere and equate it to volume rise to get the radius, then multiply by two to get the diameter.
- Akshit, akshit0201@gmail.com

(Among the first five who also got it right are: Saifuddin S F Khomosi, saif_sfk@hotmail.com; Saurabh Sunil, saurabhsunil7@gmail.com; Priyamvada Vishwamitra, priyammysore@gmail.com; Hana Mustafa, hanahish@gmail.com; Aaditya Shankar Natarajan, aaditya.shankar.n@gmail.com.)

ENDGAME(S)
1. Although the Celsius and centigrade scales are the same today, originally there were two differences between them. (One of them is easy to Google, the other isn't.)
2. Bowler bowls, batsman misses, ball misses wicket, keeper can't collect, ball keeps going. Batsmen go for a run, fielder fields ball, throws it to keeper who, before non-striker can make it to crease, whips the bails off. Who's out: striker stumped or non-striker run out?

(Mukul can be reached at mukul.mindsport@gmail.com)

• Mindsport