2 5
_ G G S
W _ R _
B R _ K _ N .
T H _ R _
_ S
_ N L Y
_ N _
W _ Y
_ F
F _ N D _ N G
_
S _ L _ T _ _ N
T _
T H _ S
P R _ B L _ M :
N _ M B _ R S
W H _ C H
L _ _ V _
_
R _ M _ _ N D _ R
_ F
1 ,
W H _ N
D _ V _ D _ D
B Y
2 :
3 ,
5 ,
7 ,
9 ,
1 1 ,
1 3 ,
1 5 ,
1 7 ,
1 9 ,
2 1 ,
2 3 ,
2 5 ,
2 7 ,
2 9 ,
3 1 ,
3 3 ,
3 5
N _ M B _ R S
W H _ C H
L _ _ V _
_
R _ M _ _ N D _ R
_ F
1 ,
W H _ N
D _ V _ D _ D
B Y
3 :
4 ,
7 ,
1 0 ,
1 3 ,
1 6 ,
1 9 ,
2 2 ,
2 5 ,
2 8 ,
3 1 ,
3 4 ,
3 7
N _ M B _ R S
W H _ C H
L _ _ V _
_
R _ M _ _ N D _ R
_ F
1 ,
W H _ N
D _ V _ D _ D
B Y
4 :
5 ,
9 ,
1 3 ,
1 7 ,
2 1 ,
2 5 ,
2 9 ,
3 3 ,
3 7
N _ M B _ R S
W H _ C H
L _ _ V _
N _
R _ M _ _ N D _ R
W H _ N
D _ V _ D _ D
B Y
5 :
5 ,
1 0 ,
1 5 ,
2 0 ,
2 5 ,
3 0 ,
3 5
T H _
_ N L Y
N _ M B _ R
F _ L F _ L L _ N G
T H _
F _ _ R
C _ N D _ T _ _ N S
_ S
2 5 Clue
25 EGGS WERE BROKEN. THERE IS ONLY ONE WAY OF FINDING A SOLUTION TO THIS PROBLEM: NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 4: 5, 9, 13, 17, 21, 25, 29, 33, 37 NUMBERS WHICH LEAVE NO REMAINDER WHEN DIVIDED BY 5: 5, 10, 15, 20, 25, 30, 35 THE ONLY NUMBER FULFILLING THE FOUR CONDITIONS IS 25 HE HAD 15 EGGS. THE FIRST PERSON BOUGHT HALF OF THE 15 EGGS WHICH IS 7½ EGGS AND ANOTHER ½ EGG. SO HE BOUGHT 8 EGGS IN TOTAL AND JACK IS LEFT WITH 7 EGGS. THE SECOND PERSON BOUGHT HALF OF THE REMAINING 7 EGGS WHICH IS 3½ EGGS AND ANOTHER ½ EGG. SO HE BOUGHT 4 EGGS AND JACK IS LEFT WITH 3 EGGS. THE LAST PERSON BOUGHT HALF OF THE REMAINING 3 EGGS WHICH IS 1½ EGGS AND ANOTHER ½ EGG. SO THE LAST PERSON BOUGHT 2 EGGS. THAT LEAVES 1 EGG REMAINING IN JACK'S BASKET THE IDOLS FROM LEFT TO RIGHT ARE: GOD OF DIPLOMACY, GOD OF FALSEHOOD, GOD OF TRUTH. THE GOD OF TRUTH IS NOT SEATED ON THE LEFT BECAUSE HE ALWAYS SPEAKS THE TRUTH WHEREAS THE IDOL ON THE LEFT REPLIED THAT THE GOD OF TRUTH IS SEATED AT THE CENTRE. THE GOD OF TRUTH IS ALSO NOT SEATED IN THE CENTRE AS HE ALWAYS SPEAKS THE TRUTH BUT THE IDOL AT THE CENTRE REPLIED THAT THE GOD OF DIPLOMACY IS SEATED AT THE CENTRE. THEREFORE, THE GOD OF TRUTH IS SEATED ON THE RIGHT. AS GOD OF TRUTH IS SEATED ON THE RIGHT, AND HE ALWAYS SPEAKS THE TRUTH, THEN THE THE GOD OF FALSEHOOD IS SEATED AT THE CENTRE. THE GOD OF DIPLOMACY IS SEATED ON THE LEFT AND HE HAS LIED THE CHILDREN ARE 1, 6 AND 6 YEARS OLD. THE PRODUCT OF THEIR AGES IS 36, SO NONE OF THEM CAN BE OLDER THAN 36. THE NUMBER 36 HAS TO BE EXPRESSED AS THE PRODUCT OF 3 NUMBERS. THEIR POSSIBLE AGES ARE (THE SUM OF THEIR AGES IS IN BRACKETS): 1, 1, 36 (3938) 1, 2, 18 (21) 1, 3, 12 (16) 1, 4, 9 (14) 1, 6, 6 (13) 2, 2, 9 (13) 2, 3, 6 (11) 3, 3, 4 (10) SINCE CHERYL IS TOM'S NEXT DOOR NEIGHBOUR, TOM KNOWS CHERYL'S HOUSE NUMBER. TOM WOULD KNOW THE CHILDREN'S AGES IN EVERY CASE THAT SUMS UP TO A UNIQUE NUMBER EXCEPT FOR THE SUM OF 13, WHICH HAVE 2 COMBINATIONS OF POSSIBLE AGES. AS A RESULT, TOM WOULD BE CONFUSED AS HE HAS TO PICK BETWEEN THE 2 COMBINATIONS: (1,6,6) AND (2,2,9). CHERYL THEN TELLS TOM ABOUT HER YOUNGEST CHILD WHO LIKES STRAWBERRY MILK WHICH TELLS TOM THAT THERE IS ONLY 1 YOUNGEST CHILD