Solving the puzzle of the missing Sh1,000: how not to do accounts!
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
28 August 2016
Evans Mutuku sent me this puzzle via Twitter: “Assume you saw a laptop
costing Sh97,000, [but] you didn't have the cash. So you borrowed
Sh50,000 from [your] mom and Sh50,000 [from your] dad = Sh100,000. You
[then] bought the laptop which left you with Sh3,000 change. You gave
your dad Sh1,000 and your mum Sh1,000 and kept the other Sh1,000 to
yourself.
“Now you owe your mum Sh49,000 and your dad Sh49,000 = Sh98,000. [Add
the] Sh1,000 [you] kept [and the total is] Sh99,000. Where is the
missing Sh1,000?”
This puzzle is similar to the one I solved here slightly more than ten
years ago. In the older one, three people go to a hotel an order a meal
costing Sh30. They contribute Sh10 each and give the waiter a total of
Sh30. The waiter goes to the cashier and is informed that the meal was
actually Sh25 and not Sh30. He is given five one-shilling coins to give
back to the three customers.
He pocketsSh2 and gives each man Sh1. Now, each man paid Sh9 making a
total of Sh27 (9 x 3 = 27). Add the Sh2 kept by the waiter and the total
comes to Sh29. Where is the missing shilling?
If you want to get the solution to the second puzzle, then go to the
nearest library and dig out the newspaper of 28th May 2006!
For now, I will explain what’s going on in Mutuku’s problem.
The first question to ask about Mutuku’s puzzle is the importance of
stating that you borrow Sh50,000 from mum and Sh50,000 from dad: Does
the situation change if we said that you borrowed Sh100,000 from your
parents? No it doesn’t.
In fact, in the eyes of an accountant, it doesn’t matter whom you borrow
from; the only important fact is that the Sh100,000 is borrowed. That
is, it is not your money. The only reason the borrowing is split into
two is to help in confusing the listener!
Immediately after borrowing the money, you owe your parents Sh100,000;
but you have Sh100,000 in your pocket. Therefore, your balance sheet is
balanced. You are NOT bankrupt!
You go to the shop and buy a Sh97,000-laptop and are left with Sh3,000
cash. Up to this moment you still owe your parents Sh100,000; but now,
you own a Sh97,000 computer and you have Sh3,000 in your pocket. So,
again, what you have is equal to what you owe.
When you pay back Sh2,000 to your parents, you are left owing them
Sh98,000 and you have Sh1,000 in your pocket. Up to this point, my
numbers are tallying with Mutuku’s calculations. But in the next step,
he does something inexplicable: he adds the Sh1,000 you have to the
Sh98,000 you owe.
There is no
justification for doing that! You cannot and should never add what you
have (in your pocket) to what you owe. The money in your pocket is part
of what you have: that is, a Sh97,000 computer and Sh1,000 in cash. The
total is Sh98,000. This is exactly equal to the Sh98,000 that you owe
your parents. Quod
Erat Demonstrandum!
 |
 |