**"Estimate the length of this table"**

He thought for a while observing the table and said, “More
than 45 inches and less than 75 inches.”

“How did you guess?”

“Our small scale is of 15 inch. I feel around 3 and half
such scales will fit along the table.”

(Can you figure out his two errors? What will YOU do in this
case? Take some time to think about your strategy before your read ahead)

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“Yes, I agree with you that around 3 and half scales would
fit along the table. However, can you explain how you got these two figures: 45 and 75?”

“Sir, 15 x 3 = 45 and 15 x 4 = 75.”

After some thinking – “What if it were exactly 5 scales?”

"Then it would be 90 inches."

“What if it were 10 scales?

"15 x 10 = 150 inches."

“Okay… So you mean 10
scales would mean 150 inches and 5 scales would imply 90 inches….”

While he was about to nod in agreement, he paused…. I could
see him being puzzled at something….

After 3-4 seconds: “What happened?”

“Sir, wait… I think there is some problem.”

“What problem?”

**“Some problem in the table of 15.”**

“Oh, is it? How do you know?”

*(I also succeeded in NOT reacting to his response with my laughter/ shock/ anger)*

“Because 15 x 10 = 150, then how can 15 x 5 = 90?”

“Hmm…. So then, what is the contradiction according to you?”

“If 15 x 5 = 90, then 15 x 10 should be double of 90 i.e.
180.”

“True… So then…….? Is
15 x 10 = 150 or 180?”

“180 does not seem to be correct……150 is correct.”

“Hmmm…. So?”

“But then 15 x 5 = 90 is also correct…..Table of 15 has
something special it seems…. This is surprising, I never saw this…”

I just ensured that
he found an authentic enquirer along with him in this process/ problem.

“Can we check other tables also then?”

“Yes… 12 x 10 = 120……. 12 x 5 = 60…. Here it is working
properly….”

“Working means?”

“Means 60 is half of 120…”

“Okay….. So?”

“Wait Sir…. Let me check some more…… 11 x 10 = 110 and 11 x 5 = 55…… Here also, it’s working
well…”

“Hmm…… Should we check some more tables…?”

“No sir… I feel it should work in the table of 15 also
then…. 15 x 5 should be half of 15 x 10…….? I am not getting why we are not
getting so in 15?”

“Okay… Let’s recite the table of 15 together….” (Why would I have done so? Was there any
other way?)

“15x 1 = ……”

“15”

“15x 2 = ……”

“30”

“15 x 3 = ……”

“45”

“15 x 4 = …….”

“75”

“15 x 5 = ……..”

“90”

“15 x 6 = …….”

“90”

I paused, waiting for him to pick up the clue….. And Yes! He
did it!

“Sir, Wait… I think I have done some mistake… How can 15 x 5 and 15 x 6 be both 90?”

“Hmmm….. So?”

He started telling the tables again but slowly and more
thoughtfully this time. I could see him making the table of 15 via repeated
addition (adding 15 to the previous multiple).

“Sir, I got the mistake!!
I had missed out 60.”

**The JOY of Discovery on his face was unmatchable!!**

“Hmmm…. So…? What about the mistake in the table of 15….?” (This time, I couldn’t hide my teasing smile :-)

And even he continued to laugh -- with little shades
of embarrassment :-)

Rupesh Gesota

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