Did you solve it? Are you smarter than a 12-year-old? | Mathematics

Earlier today I set you up with three puzzles for 12 year olds, which are used by the charity Axiom Mathematicswhose mission is to help top-achieving, low-income children continue to perform well throughout high school.

1. Backward multiplication

Which four-digit number reverses itself when multiplied by 4? As in, what are the numbers a, b, c and d such that the number abcd x 4 = dcba?

(In this problem, the letters a, b, c and d all stand for different numbers.)

Solution 2178 x 4 = 8712

STEP 1 a can only be 1 or 2, because four times a number greater than 3000 will be greater than 12,000, so has five digits, not four;

STEP 2 The solution must be even (since all multiples of 4 are even) and so on a should be 2.

STEP 3 We know that 4 xd is a number that ends in 2. Working through the four times table we arrive at d = 3 or 8

STEP 4 d can only be 8 or 9, since 4 x 2 thousand and something is at least 8 thousand and something; so d is 8; so 4x b (possibly plus a carry) is less than 10, otherwise d should be 9, so b = 1 or 2, and must therefore be 1 since it must be different from a.

STEP 5. c x 4 + carry of 3 has one digit 1, so c x 4 has units digit 8, so c can only be 2 or 7 and must therefore be 7 since it must be different from a.

2. Really secret Santa

A group of nine secret agents: 001, 002, 003, 004, 005, 006, 007, 008 and 009 organized a Secret Santa. The instructions are coded to keep the donors secret.

• Agent 001 gives a gift to the agent who gives a gift to agent 002

• Agent 002 gives a gift to the agent who gives a gift to agent 003

• Agent 003 gives a gift to the agent who gives a gift to agent 004

• and so on, until

• Agent 009 gives a gift to the agent who gives a gift to agent 001

Which agent will Agent 007 get her gift from?

Solution 002

The easiest way to do this is to draw a circle and then fill it in.