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Chris Smith - Palindromes are numbers, or words, that are the same front to back, or should that be back to front?

This problem is about percentages and the numbers are palindromic. But it’s not just the numbers in the question that are palindromes.

Mr Bob Hannah is the owner of a gadget shop called Universal Palindromes Unlimited - UPU for short.

Bob has a sale on. At first he offered a WOW discount of 55% off. (55 is a palindrome).

Now he’s reduced the prices further by a Manager Special amount of £10.01. (You guessed it - another palindrome).

Otto bought a nice set of headphones from Bob for a very reasonable (and palindromic) £44.44.

But how much cash would Otto have needed to part with if he’d bought the headphones at full price with no discount?

You know Bob Hannah loves palindromes. Do you think the answer might be a palindrome too?

Remember, you know the final price and you know the discounts, so you’re going to need to work backwards to see if you can find the original price.

Can you work it out?

Chris Smith: How did you get on?

Did you spot some more palindromes?

The key to this problem is adding the discounts back onto the price in reverse order.

Kenny bought the headphones at a discounted palindromic price of £44.44.

First add Bob’s Special Price discount of £10.01.

£44.44 plus £10.01 equals £54.45.

Did you notice £54.45 is also a palindrome

We know the WOW discount price took 55% off the full price.

So £54.45 is what is left when you take 55% away from 100%. It’s 45% of the full price.

We know that when we say 45 per cent of a number what we really mean is multiply it by 45 divided by 100. But what was that original number?

To reverse the percentage, we need to divide instead of multiply. Dividing by a fraction is the same as multiplying by its reciprocal.

So we can just flip the fraction upside down.

We multiply £54.45 by 100/45

Giving a final full price of £121

You guessed it – another palindrome!