Difficulty: Tricky
Right before the bell rings, Jeri’s teacher throws up a problem on the board:
“I’m thinking of a number. When I add its digits together and multiply by seven, I get the number I first thought of.
“The number is under 40.“
Can you help Jeri find the number before class is dismissed?
Need a hint?
To get the number, you have to multiply by seven. So the number is in your seven times table!
Brainteaser answer
Jeri’s answer is 21. Because the sum of its digits, 2 + 1, is 3, and 3 times 7 equals 21.
You have to calculate the number by multiplying by 7. That means the number must be in your seven times tables, like 7, 14, 21, 35 and so on.
We also know it’s less than 40, so there are only 4 possibilities to check. Let’s start with the smallest.
The digit sum of 7 is 7. But multiply it by 7 and you get 49, not 7.
The digit sum of 14 is 1 + 4 = 5. But multiply 5 by 7 and you get 35, not 14.
The digit sum of 21 is 2 + 1 = 3. Multiply 3 by 7 and you get 21, the number you first thought of!
And just for completeness: the digit sum of 35 is 3 + 5 = 8. But multiply 8 by 7 and you get 56, not 35.
There’s also a sneaky second answer: 0
Its digit sum is zero, and multiplying by seven gets you zero again!
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