One of our colleagues spotted this apparently tempting offer in Japan. Scroll down to read how listeners have solved the mystery.
First, here are some more photos of statistically dubious signs that have been sent in by listeners.
Here is a photo of a curious light bulb offer - taken by Andrew Currie.
"1 pack 49p" (meaning 1 bulb) and next to that "5 for 40p - you save £2.05"
Surely it means 40p EACH if 5 are bought - saving 45p?
No - it really was 1 bulb for 49p or 5 bulbs for a total of 40p!
This sign tops our one from Japan - it was spotted in India and sent to us by George Miller:
"I believe I have found an offer even more enticing offer than 100% off! A friend from India sent me the attached photo, it's quite a bargain!"
This photo was sent in by Dave Bailes:
"This advert was seen in the window of a 17th century building being refurbished in Gloucester. Seems like arithmetic was not the writer's strong subject!"
If you have your own examples of innumerate adverts and signage, we would love to see them. Our email address is: firstname.lastname@example.org
All is revealed...
We have now solved the mystery of the "100% off" sign. Read the explanations and suggestions sent in by our listeners below.
I have been told that it's a store promotion where people who enter get a ticket that gives them "up to" 100% off... Connor Jenkinson
It says "up to 100% off". According to the notice there is a lottery type draw, and depending on the ticket you draw you can get a discount. The best winning ticket gives you 100% off - i.e. the goods for free. The Japanese are actually rather good at maths in my experience and by no means silly. An illustration of it being best not to draw conclusions until you are in possession of all the facts I think. Robert Charlesworth
The advert you show indicates that if you enter a lottery in the shop and win, your purchase will be 100% discounted, i.e. free of charge. Normally for this type of promotion a hexagonal barrel has red and white plastic balls in. The box is rotated and has a device that allows one ball out at a time when it is at the bottom of its rotation. A white ball coming usually means you have lost, a red ball means you win the prize - in this case a 100% discount. The shop keeper obviously controls the odds in their favour!Tony Ford
The sign saying "100% OFF!!" is obviously an advertisement for an enthusiastic hairdresser. Stewart Ware
The sign says that there is a lottery and the most that can be won is 100% off. It says ask staff for details. Probably one can win a prize of 5% off the goods that they are selling or 10% off and so on and there is a top prize of a free item. Most likely one can have a lucky dip when one buys the item and one may win a discount. One lucky winner might get the product free. David Price
BBC Radio 4's More or Less is broadcast on Friday, 4 September at 1330 BST and repeated on Sunday, 6 September at 2000 BST.
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