WORLD OF FIGURES: How not to account for your finances

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.

PHOTO | FILE |

What you need to know:

  • 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.

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 10 years ago. In that puzzle, three people go to a hotel and order a meal costing Sh30. They contribute Sh10 each and give the waiter Sh30. The waiter goes to the cashier and is informed that the meal was actually Sh25 and not Sh30. He is given Sh5 in coins to give back to the three customers.

He pockets Sh2 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, visit the nearest library and dig out the newspaper of May 28, 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.

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 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 (which is what had to be proved)!