## Teaser 2983: Maths for dessert

**From The Sunday Times, 24th November 2019** [link]

George and Martha have their five daughters round the dinner table. After the meal, they had ten cards numbered 0 to 9 inclusive and randomly handed two to each daughter. Each was invited to form a two-digit number. The daughter drawing 0 obviously had no choice and had to announce a multiple of ten.

However, the others each had the choice of two options. For example if 3 and 7 were present, either 37 or 73 would be permissible. George added up the five two-digit numbers (exactly one being divisible by 9) and Martha noticed that three of the individual numbers divided exactly into that total.

What was the total of the remaining two numbers?

[teaser2983]

## Jim Randell 5:16 pm

on22 November 2019 Permalink |This Python program runs in 114ms.

Run:[ @repl.it ]Solution:The sum of the numbers that do not divide into the total is 147.The numbers are: 14, 28, 50, 63, 97.

Of these only 63 is divisible by 9.

The sum of the numbers is 252, which is divisible by 14, 28, and 63.

And the remaining numbers (50 and 97) sum to 147.

LikeLike

## GeoffR 9:47 am

on25 November 2019 Permalink |LikeLike

## GeoffR 7:56 am

on28 November 2019 Permalink |LikeLike