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#185 Cheque out

Set by Mary Ellis

Eccentric Aunt Marion has given up buying presents for her nephew Matthew and has decided instead to gift him the annual interest she earns on her building society account. She hands him a cheque.

Matthew has never seen a cheque before and doesn鈥檛 have a bank account, so his aunt tells him to go and cash it at a post office for notes and coins.

But the cashier is clearly as baffled by cheques as Matthew, because in producing the cash, she switches the pounds and pence. Matthew sticks the money in his empty wallet without counting it and heads out to treat himself to a burger that costs 拢7. It is only then that he counts how much cash he has left. Remarkably, it is exactly twice as much as the figure on the original cheque. It is almost as if he has a magic wallet.

How much does he still have available to spend?

Solution next week

#184 Cipher sum

Solution

We can denote the sum as: ABCDE + EBEBA = DAFCB. Note that the first and last columns involve addition of A + E, but add to different numbers, which means that B + B must be > 10, with 1 carried to the next column to the left. In other words, D = B + 1, and B > 6. B can鈥檛 be 9, as it would mean that D has to be 10, and can鈥檛 be 8 because that would mean D = 9, so C would be 7 (fourth column), but that rules out any options for F. That leaves B = 7, so D = 8 and C = 5, which leads to:

47583

+ 37374

__________

84957