Here's The Answer To That Impossible Quant Interview Question

maths problem tbi

Recently we posted a difficult interview question that an employer asked an interviewee for a quant position at UBS.

The question:

The number 1978 is such a number that if you add the first 2 sets of numbers, you’ll will get the middle 2 sets of numbers. So in 1978, 19+78=97; so the question is write a formula that can find numbers that satisfy these conditions.

Most people would consider it hard, particularly the part about being asked to solve it on the spot, but a number of quants (who we might add are already employed!) clearly did not.

A number of them emailed us with the answer.

“It’s not that hard. I did it in my head,” a Ph.D. told us.

Well, well! We remain impressed with the answers, which varied somewhat but basically looked like the one below, a fail proof formula, which was derived by a user at QuantNet, a Clusterstock Contributor:

(these are digits), where

, and

. e.g., 1978 is gotten by picking x=1, y=9.

A PhD who emailed us the answer provides two examples: 

  • One example is 1978, where a=1, b=9, c=7 and d = 8 and indeed 10*1 + 9*7 +8 = 81 = 9*9.
  •  Another example is 1208, with a=1, b=2, c=0 and d=8 we get 10*1 +9*0 + 8 = 18 = 9*2.  And indeed  12+8 = 20, the middle two digits.

Our own intellectual inferiority aside, the fact that so many people emailed us with their “this is easy!” remarks and correct answers is great news. Last week at the CNBC Delivering Alpha conference, a hedge fund manager spoke with great concern about the dumbing down of America’s young citizens. Of course we can’t be sure that they were young, but most people who emailed us had stereotypical American names (with Ph.D.s at the end).

And just when we thought we couldn’t be more impressed, we got this answer, from a user who found not only the correct formula, but that there are 55 numbers that meet the conditions and that if you add 1+ all of the solutions that begin with 0, + the solutions that begin with 1 + the solutions that begin with 2, you get… 55! Neat. (Also cool, there are 9 sequential pairs after 0. And 9 is the limit.)

Want more? Check out these Wall Street interview questions >

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