You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

14 Divisors

What is the smallest number with exactly 14 divisors?

problem icon

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Jam and Egg Sandwich

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

 
Since the answer is not the same as $EGG$, $E$ is not $1$. However, $E \times E$ is less than $10$, as the answer has only three digits, so $E$ is $2$ or $3$.

The units column must carry, otherwise it would be the same as the tens column, and $A$ and $M$ are different. But this means the tens column must also carry.

But, if $E=3$, then this carry means $J = 10$, which cannot happen. Therefore $E=2$.

Since the tens column carries, $J=5$. For the carries in the tens and units columns, $G$ must be at least $5$. Trying each of these combinations leaves two of the letters having the same value, unless $G=8$. This gives $E=2,G=8,J=5,A=7,M=6$, with $288 \times 2 = 576$.
 

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem