Puzzle of ₦51 Instead N50 – Where N1 Came From? (SEE RIDDLE SOLUTION)
I have explained this puzzle several times in the past, but it seems the question keeps resurfacing every now and then like Eke Market Days 😀 So, let me just plug the answer to the riddle here – then I can refer whoever again asks me same question, to this page.
The short answer to the riddle is – There is no actual extra Naira!
This puzzle can carry any currency, but it’s still the same question from around 1933. The long answer is to break it down properly, ie. rearrange the answer to get the figures correctly. Before my personal answer (which is the easiest to understand), I found two interesting answers, one from Wikipedia below:
The actual solution to this riddle is to add correctly (correct time, correct person and correct location) from the bank point of view which in this case seems to be the problem:
First day: $30 in the bank + $20 owner already withdrew = $50
Second day: $15 in the bank + ($15 + $20 owner already withdrew) = $50
Third day: $6 in the bank + ($9 + $15 + $20 owner already withdrew) = $50
From the owner point of view the correct solution is this:
First day: $20 owner already withdrew + $30 in the bank = $50
Second day: $20 owner already withdrew + $15 owner already withdrew + $15 in the bank = $50
Third day: ($20 owner already withdrew + $15 owner already withdrew + $9 owner already withdrew) + $6 in the bank = $50
The solution appears very obvious if the owner withdraws every day only $10 from $50. To add up 40 + 30 + 20 + 10 using the same pattern from above would be too obviously wrong (result would be $100).
And the second from Presh, from MindYourDecisions website:
Suppose a person spends 50 in a series of four transactions s1, s2, s3, s4. The corresponding balances would be:
| Spend | Balance |
| s1 | 50 – s1 |
| s2 | 50 – s1 – s2 |
| s3 | 50 – s1 – s2 – s3 |
| s4 | 50 – s1 – s2 – s3 – s4 |
| Sum of spending | Sum of balances |
| s1 + s2 + s3 + s4 | 200 – 4s1 – 3s2 – 2s3 – s4 |
Notice the sum of the balance column is:
200 – 4s1 – 3s2 – 2s3 – s4
There is no reason this sum has to be 50. In the original problem with s1 = 20, s1 = 15, s1 = 9, and s1 = 6, it just works out the sum of the balance column is 51.
And now, to my own answer. I have it in a picture format – as they say, a picture is worth a thousand words: there you have it!
